91 comments

  • Thursday, Jul 11, 2024

    TL;DR, Some Tips:

    "MOST"/"SOME" before "ALL", is a Valid call ; "ALL" before "MOST"/"SOME, is Invalid and hurts my tum.

    ----------------

    I went through the Review of Valid Formal Arguments in the last section and this Review of Invalid Formal Arguments and grouped concepts a bit differently than 7Sage. It's easier for me to understand opposite/competing rules by placing them side-by-side rather than trying to learn valid arguments in one go and invalid arguments in another go. I hope this helps others! Writing this all out reinforced the concepts for me.

    -----------------

    For all of these, I used the following ideas to better follow 7S's A→B→C set of examples:

    A = Apes

    B = Brave

    C = Cool

    x = Xander, an Ape

    y= Yara, a human

    xxxxxx GROUP 1 VALID ARGUMENTS xxxxxx

    The Conditional Argument

    A → B

    (x)A

    ----therefore----

    (x)B

    All apes are Brave. Xander is an ape. Xander is brave. VALID.

    The Contrapositive Argument

    A → B [CONTRAPOSITIVE: /B → /A]

    (y)/B

    ----therefore----

    (y)/A

    All apes are brave. Yara is not Brave. Yara is not an ape. VALID.

    xxxxxx GROUP 1 INVALID ARGUMENTS xxxxxx

    Confusing Sufficiency for Necessity

    A → B

    ----therefore----

    B → A

    All apes are brave. All brave things are apes. INVALID. Some brave things could be non-apes, like human people studying for the LSAT.

    Denying the Sufficient Condition

    A → B

    /A

    ----therefore----

    /B

    All apes are brave. If you're not an ape, you're not brave. INVALID. As in the other invalid argument form, we could point to non-apes that are brave, like you, future test-taker!

    Affirming the Necessary Condition

    A → B

    B

    ----therefore----

    A

    All apes are brave. If you're brave, you're an ape. INVALID. Just because you have the necessary condition of being brave does not affirm that you have the sufficient condition of being an ape. Again, what if the brave thing is you, a human?

    I suspect that was the easier part of these lessons for most of us to track. Moving on to the part I had to review three times...

    xxxxxx GROUP 2a VALID vs INVALID ARGUMENTS xxxxxx

    VALID re "MOST"

    Conditional Chaining [Remember this is a chain of "all" statements, just helpful to see it against the various "most" and "some" valid/invalid arguments.}

    A → B → C

    ----therefore----

    A → C

    All apes are brave and all brave things are cool, therefore all apes are cool. VALID.

    Most Before All

    A —m→ B → C

    ----therefore----

    A —m→ C

    Most apes are Brave. All brave things are cool. Therefore, most apes are cool. VALID.

    Two Mosts

    A —m→ B

    A —m→ C

    ----therefore----

    B ←s→ C

    Most apes are brave. Most apes are cool. Some brave things are also cool. VALID.

    INVALID re "MOST"

    Most Statements are Not Reversible

    A —m→ B

    ----therefore----

    B —m→ A

    Most apes are brave. Most brave things are apes. INVALID. What if there are billions of brave people, but only a few thousand brave apes?

    All Before Most

    A → B —m→ C

    ----therefore----

    A ←s→ C

    All apes are brave and most brave things are cool. Therefore some apes are cool. INVALID. Imagine we collect one billion cool things: tech equipment, scientific discoveries, Olympic medalists, yo-yos, and even a bunch of cool animals. Is it true that at least one of those cool things MUST be an ape? No, not based on this information alone. It COULD be true but it isn't a MUST be true. And "SOME" requires AT LEAST ONE.

    Most Before Most

    A —m→ B —m→ C

    ----therefore----

    A ←s→ C

    Most apes are brave and most brave things are cool, therefore some apes are cool. INVALID. I think 7S's explanation of why these are all similarly flawed is sound, so I wont repeat myself this is already soooo long I'm sorry.

    xxxxxx GROUP 2b VALID vs INVALID ARGUMENTS xxxxxx

    VALID re "SOME"

    Conditional Chaining [Remember this is a chain of "all" statements, just helpful to see it against the various "most" and "some" valid/invalid arguments.}

    A → B → C

    ----therefore----

    A → C

    All apes are brave and all brave things are cool, therefore all apes are cool. VALID.

    Some Before All

    A ←s→ B → C

    ----therefore----

    A ←s→ C

    Some apes are brave. All brave things are cool. So, some apes are cool and also some cool things are apes. VALID. There are 100 apes, they're all brave and that makes them all cool. That means that some (more than some, all, actually) apes are indeed cool but also in the world of total cool things, the apes have to be included.

    INVALID re "SOME"

    All Before Some

    A → B ←s→ C

    ----therefore----

    A ←s→ C

    All apes are brave. Some brave things are cool. Therefore, some apes are cool. INVALID. Sadly if we were creating an intersection of brave things and cool things, we know the apes would be in the "brave things" circle, but there's no rule here that implies those brave apes intersect with the section of "cool things." Only SOME brave things are cool. Maybe it's just yo-yos and Olympic medalists and nothing else.

    Some Before Some

    A ←s→ B ←s→ C

    ----therefore----

    A ←s→ C

    Some apes are brave. Some brave things are cool. Therefore, some apes are cool. INVALID. 2 apes are brave. 13 things are cool, they're all yo-yos. No apes, in this situation, are cool, it's not enough to make an inference with this information.

    117
    Saturday, Oct 5, 2024

    this was SO helpful!! It finally clicked for me!!! I agree, having all these chains in one place makes it easier to memorize the logic.

    1
    Friday, Aug 2, 2024

    this is amazing, and so much easier to understand. Thank you!

    0
    Sunday, Feb 9, 2025

    This was legitimately BETTER than the whole lesson lol

    0
    Friday, Oct 25, 2024

    Thank you! SO Helpful :)

    0
    Tuesday, Apr 29, 2025

    Thank you so much!

    0
    Tuesday, Jul 30, 2024

    thankuuuu!!!

    0
    Thursday, Aug 22, 2024

    you are amazing!

    0
    Thursday, Sep 5, 2024

    Thank you so much, all the examples of invalid arguments just confused me more than it helped me. This clarified a lot of things for me!!

    0
    Friday, Jul 19, 2024

    This is amazing thank you so much

    1
    Friday, Jul 12, 2024

    Thank you!

    3
    Thursday, Aug 8, 2024

    THANK YOU SO MUCH OMG I was on the edge of crying thank you and 7S shame on yall for not having the foundation fully explained with videos

    9
    Tuesday, Oct 15, 2024

    can I send my money to u instead of 7S

    3
    Thursday, Feb 12

    @nirvanahabash219 what about

    most cool things are apples. And most apples are yellow. Therefore, some things that are yellow are also cool.

    1
  • Sunday, Mar 16, 2025

    I honestly don't think this lesson sucks at all. As DAVEMARINO said below, you need to have a strong grasp of the lessons on sets. I too was having problems recognizing formal logic flaws in drill and preptest questions until I went back and reviewed both of the sections on sets. One thing that significantly helped me was to write down each of the 8 formal logic flaws on a separate piece of paper (with their examples and Lawgic forms) and have this paper next to me as I drilled. Having the flaws in open view as I drilled helped to facilitate my pattern-recognition of these flaws whenever they appeared in questions. Eventually, you begin to recognize them instinctively. Above all, practice practice practice.

    55
    Tuesday, Aug 5, 2025

    @gabrielfermin54 this sounds like a really great way to drill, thanks for the advice!

    0
  • Monday, Dec 9, 2024

    This section on flaws needs some serious work. Videos would help clarify things to a greater degree than these pitifully written explanations. I had to go to another site to get clarification.

    41
    Saturday, Dec 21, 2024

    .

    0
    Saturday, Dec 21, 2024

    exactly!! same

    #feedback

    0
  • Thursday, Oct 2, 2025

    I just don't understand how the grammar lesson had so many thorough explanations with videos but not this lesson... very disappointing

    37
    Yesterday

    @ArielleSambolin I was wondering the same thing. I didn't need a video on what is a subject, noun...etc..

    1
  • Tuesday, Sep 3, 2024

    #feedback I feel it would be helpful to also include what the valid form of the arguments are so that in the review we can have a quick way to reference a valid/invalid argument for example, and see how the test writers try and trick us.

    29
  • Tuesday, Aug 20, 2024

    A skill builder of this would be nice

    25
    Friday, Sep 20, 2024

    #feedback

    SKILL BUILDER PLEASE!!!!!

    4
  • Friday, Jan 5, 2024

    we'll never run out of invalid arguments because, as I'm starting to realize on an increasingly painful level, the world is filled with invalid arguments.

    23
  • Wednesday, Mar 4

    we WILL avoid trap answers, everybody 180

    21
  • Sunday, Dec 14, 2025

    I know that the lack of videos made this set a bit hard to understand so here are my explanations that helped me understand. They are super dumbed down because I am dumb so hope it helps

    Sufficiency for Necessity

    A->B

    ----

    B->A

    • WRONG. Why? Imagine this, All cats are mammals SO, all mammals are cats. Is this conclusion that all mammals are cats correct based off the premise that all cats are mammals. NO! The only thing the premise is telling us is that cats are mammals. We have no clue what mammals are and thus cannot say that mammals are cats because we would be confusing sufficient and necessity

    Denying Sufficient Condition

    A->B

    /A

    --

    /B

    • Wrong. Why? Just because we deny the sufficient condition does not mean that the necessary condition is false. Remember from the earlier lessons that, Membership in the subset is sufficient for membership in the superset, but it's not necessary.

    • Example. All cats are mammals. Steve the lion is not a cat. Therefore, Steve the lion is not a mammal. Does the premise being true make the conclusion true? Is this valid? NO IT's NOT. All we know is that Cats are mammals. Steve the lion isn't a cat, ok cool that's fine, BUT does that mean he's not a mammals? We don't know. The premise doesn't tell us anything about Steve the lion not being a mammal.

    Affirming the necessary condition

    A->B

    B

    --

    A

    • Wrong. Why? Just because we say the necessary condition is true does not immediately mean that the sufficient condition is true. Remember back to subset and superset. The circle within the circle. Just because I'm in the first circle does that mean I'm in the second one? NO.

    • Example. All cats are mammals. Steven the lion is a mammal. Therefore, Steve the lion is a Cat. Does this premise being true make the conclusion true? Is this valid? NO! Just because Steve the lion is a mammal tells us nothing about if he is a cat or not. Maybe to become a cat one needs to have stripes and Steve the lion doesn't have strips so we can't say that just because he satisfies the necessary condition that he is cool with the sufficient condition.

    Most statement are not reversible

    A-m->A

    --

    B-m->A

    • Wrong. Why? Just because most A are B, does not mean most B are A.

    • Example. Most cats are mammals. Therefore, most mammals are cats. Based off the premise of "most cats are mammals" can we say it's valid that most mammals are cats? NO WE CAN'T. We have no clue what most mammals are. All we know is that most cats are mammals

    20
    Sunday, Dec 14, 2025

    @Student101 Part 2 to follow up on these

    All before Most

    A->B-m->C

    --

    A<-s->C

    • Wrong. Why? Lets imagine it like this. All 2 of my red cars are trucks. Most of my 100 trucks are made by ford. Therefore, some of my red cars are made by ford. I hope this helps to show were the gap is. The reason it's invalid is because we have no clue if some of my red cars are made by ford or not. Maybe 98 of my trucks (which would satisfy most) are made by ford and 2 of my trucks (the red ones) are made by 7Sage auto. Then yah we can't say that some of my red trucks are made by ford, because this is incredibly weak. It could be the change that my 2 red trucks are not part of that most that is made by ford.

    All before Some

    A->B<-s->C

    --

    A<-s->C

    • Wrong. Why? Lets imagine it like this. All of my 3 cats are from London. Some cats from London enjoy drinking tea. Therefore, some of my cat's enjoy drinking tea. This is Invalid because what if for all we know my 3 cats from London are allergic of tea.

    • Another way to think about it is like this. All A are B. Some B are C. Thus, some A are C. Think of it like exclusions and inclusions. Just because all of my A are now in B does not mean that some of those A's made it all the way to C. They could have been left behind and so we can't say that some A are C

    13
  • Wednesday, Feb 12, 2025

    [This comment was deleted.]

  • Wednesday, Jan 1, 2025

    If you didn't fully grasp the "Logic of Intersecting Sets" section, this "Formal Logic Flaws" section is useless. Though this last lesson is a nice summation.

    Would be more helpful if it was formatted the same way as LIS, and had videos.

    19
  • Saturday, Mar 2, 2024

    I have no idea if this'll help anyone, but one thing I found helpful — particularly for the first three invalid formal arguments — is to find the contrapositive and remind myself that contrapositives are logically valid. Maybe it's because I've been so steeped in Lawgic, but I'm constantly finding myself trying to find contrapositives, so much so that it's almost automatic. But, seeing a contrapositive next to the original form of an argument, and then contrasting that with the invalid formal argument listed above, really helped crystalize why the invalid arguments are, in fact, invalid.

    19
  • Edited Wednesday, Mar 4

    Here are some more complex examples of invalid arguments that you may see on the test:

    (1) Confusing Sufficiency for Necessity:

    All published constitutional scholars have advanced training in legal theory. Dr. Morales has advanced training in legal theory. Therefore, Dr. Morales is a published constitutional scholar.

    (2) Denying the Sufficient Condition:

    If a company qualifies for federal renewable-energy subsidies, then it uses solar or wind technology in its operations. GreenTech Industries does not qualify for federal renewable-energy subsidies. Therefore, GreenTech Industries does not use solar or wind technology.

    (3) Affirming the Necessary Condition:

    Any policy proposal that significantly reduces urban air pollution must limit emissions from private vehicles. The new proposal limits emissions from private vehicles. Therefore, the new proposal significantly reduces urban air pollution.

    (4) Most Statements Are Not Reversible:

    Most peer-reviewed articles in leading medical journals are written by researchers affiliated with major universities. Therefore, most articles written by researchers affiliated with major universities appear in leading medical journals.

    (5) All Before Most:

    All constitutional law professors are law professors. Most law professors publish articles on legal theory. Therefore, some constitutional law professors publish articles on legal theory.

    (6) All Before Some:

    All marine biologists working in coral reef conservation programs are members of the International Society for Marine Science. Some members of the International Society for Marine Science specialize in deep-sea hydrothermal vent ecosystems. Therefore, some coral reef conservation biologists specialize in hydrothermal vent ecosystems.

    (7) Most Before Most:

    Most urban commuters who rely on public transit read digital news during their commute. Most people who read digital news during their commute closely follow international political developments. Therefore, some urban commuters who rely on public transit closely follow international political developments.

    (8) Some Before Some:

    Some historical linguists specialize in ancient Indo-European languages. Some scholars who specialize in ancient Indo-European languages conduct field research on endangered modern dialects. Therefore, some historical linguists conduct field research on endangered modern dialects.

    16
    Edited Wednesday, Mar 4

    What helped me was to read these and if they didn't intuitively make sense, sit with them for as long as it took until it clicked.

    Write them down on paper, poke holes in the why, ask Chatgpt for more examples and drills, look up common answers for flaw questions, etc.

    4
    Edited Wednesday, Mar 4

    Another tip I got was to diagram every question or drill, even if I thought I understood it, until the patterns became intuitive. If you don't understand the reasoning, you can always memorize rules.

    4
  • Friday, May 1

    reading through this helped wayyy more than the previous lessons on the same topics

    10
    Tuesday, May 26

    @StarBrooks 100% agree, the explanation with the use of visual aid is super helpful. Wish the previous modules were similar to this one.

    2
  • Friday, Jan 17, 2025

    [This comment was deleted.]

    Monday, Feb 17, 2025

    The point of this section is to tell you that you WILL see these flaws on the test, and you need to be able to recognize them.

    The valid forms of all of these arguments have already been taught to us in previous lessons.

    22
  • Friday, Jul 12, 2024

    Does anyone know where I can find a video similar to this explanation? It is much easier for me to understand it with examples or if I hear someone explain it than it is to read

    9
    Wednesday, Aug 21, 2024

    I would look under V1 in the section "Invalid Argument Forms"!

    0
  • Friday, Jun 19

    peak examples with visuals. please someone like my comment so i can come back

    8
  • Tuesday, Mar 24

    I think this is a case where as many videos as 7Sage can make, drilling and consistent practice is the only way to master these concepts. Gotta put in the work

    8
  • Wednesday, May 27

    Where's my bestie that made those very helpful quizlets?

    7
  • Tuesday, Jun 23

    Someone reply or like this so I can come back to it if I need please!!

    6
    Wednesday, Jun 24

    @murphymurphy1818 bookmark it!

    1
  • Thursday, Jul 16

    Really appreciate the diagrams.

    5
  • Thursday, Sep 11, 2025

    if you were my greatest enemy, i would screenshot these invalid arguments and send them to you and tell you that they're valid

    5
    Monday, Sep 29, 2025

    @emilylu you're mistaken to assume your greatest enemy isn't also on 7sage's core curriculum.

    2
  • Wednesday, Jul 22

    Diagrams help solidify these quantifiers better in my head than a wall of text

    4
  • Thursday, Apr 30

    This right here is exactly why I love 7Sage, and will sing your praises until the end of time. For someone who truly learns visually, and couldn’t always connect the “lawgic” even when it was in video form from earlier once we hit the some, most, and all, inferences, these visuals helped immensely!

    4
  • Wednesday, Apr 29

    Loved the visuals❤️

    4

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