@Kevin Lin Now that I am further a long in the lessons it makes a lot more sense. Thank you for the response!

So I think for contrapositive and negation

Contrapositive: Creates equivalent statement. Compared to the original it only provides support, so this helps to make valid inferences from the original conditions.

Must be true question example: To qualify for scholarship, students must have a GPA above 3.5. Bob does not have a GPA above 3.5. (Qualify -> GPA > 3.5)

To know what must be true you need a contrapositive since it provides support to what is known. (/GPA > 3.5 -> /Qualify)

Negation: This purposefully contradicts the original statement. You need this to show what would make the original statement false.

We aren't there yet but this is useful in later lessons like Necessary assumptions to try and destroy an argument.

Maybe I just need more practice with lawgic. For both of the questions just reading in english it made sense and I got them both right. Lawgic only made them more convoluted and makes me second guess myself.

After 20mins, I think I understand it now.

Statement: "You can go to law school only if you have a bachelor's degree"

Translation: Law school → Bachelor's degree

What this means:

• Bachelor's degree is NECESSARY (required)

• But bachelor's degree is NOT SUFFICIENT (not enough by itself)

• You ALSO need: LSAT score, GPA, application, letters of rec, etc.

Question: "You have a bachelor's degree. Can you go to law school?"

Answer: We don't know! You have ONE necessary condition, but you need ALL of them (LSAT, GPA, etc.)

Vs.

Statement: "You can go to law school if you have a bachelor's degree"

Translation: Bachelor's degree → Law school

What this means logically:

• Bachelor's degree is SUFFICIENT (enough by itself)

• Having a bachelor's degree GUARANTEES law school admission

• LSAT doesn't matter, GPA doesn't matter, nothing else matters. You have any bachelors, congrats you get in!

  Question: "You have a bachelor's degree. Can you go to law school?"

  Answer: Yes!

Trying to see if I have the proper intuitive understanding.

Thinking of A → B as a domino chain.

• If domino A falls → domino B falls (guaranteed)

Thinking of xA as: Domino A just fell (we knocked it over)

• x (some specific person/thing) is in set A"

• "The sufficient condition is satisfied"

• "We knocked over the first domino"

Therefore xB: Domino B MUST fall (no choice, the chain reaction is triggered)

• "x MUST be in set B"

• "The necessary condition is satisfied"

• "The second domino fell"