The question stem says, which of the following is an assumption required by the argument?

So this is a necessary assumption question.

it is important, in order to maintain a healthy back,

to exercise the muscles on opposite sides of the spine equally.

After all, and so this phrase, after all,

tells me that this first part is a conclusion of some kind,

and that it's being supported by what comes after, after all.

So what is the reason in support of this first sentence?

Because balanced muscle development is needed to maintain a healthy back.

Since the muscles on opposite sides of the spine must pull equally in opposing directions

to keep the back in proper alignment and protect the spine.

Now this is a pretty complicated argument because what's happening here is we have this

since that is introducing a premise,

and this premise is supporting what is a intermediate or subsidiary conclusion,

which is the claim that balanced muscle development is needed to maintain a healthy back.

And then that subsidiary or intermediate conclusion is in turn supporting

the first claim, which is the main conclusion.

Now typically when this happens where we have an intermediate and a main conclusion

and I'm looking for assumptions,

I'm very focused on the jump between the intermediate conclusion and the main conclusion.

So in the first part of the explanation, that's what I'm going to focus on.

But I do know that a lot of people find this problem very difficult,

and I think it's because about what's happening with the premise

and the premise to intermediate conclusion jump.

So I'm going to come back in the second half of the explanation to address that.

So for now, let me just go ahead and diagram the intermediate conclusion to the main conclusion jump.

And the reason I'm going to diagram it is because we have conditional statements.

The intermediate conclusion is balanced muscle development is needed to maintain a healthy back.

This is needed to maintain a healthy back.

So if you want a healthy back, this is something that you need.

This is what the intermediate conclusion is saying.

You need balanced muscle development.

And based on this, the author is reaching the main conclusion,

which is that when you're exercising the muscles in your back,

it's important in order to maintain a healthy back

to exercise the muscles on opposite sides of the spine equally.

And so you can think of that as saying,

in order to maintain a healthy back,

so if you want a healthy back,

then this is something that is important.

Now technically, they just use the word important,

so it's not strictly speaking a necessary condition.

But for the purpose of the visual here,

I'm just going to equate the importance of the thing as calling it necessary.

So what's the thing that's important to do for a healthy back?

You have to exercise the muscles on opposite sides equally.

So if I were actually doing this problem for real,

this is the part of the argument that I'm focused on,

and I'd be looking for gaps in the jump from this idea to this conclusion.

Now as I mentioned, right now I'm just going to focus on the intermediate conclusion to the main conclusion.

Let's set aside the premise until later.

If you just focus on this part of the argument,

can you spot what's missing here?

Does this intermediate conclusion, does this statement here

actually prove that if you want a healthy back, it's important to exercise muscles equally?

And once you get more experience with logical reasoning,

you'll recognize that the idea of exercising muscles equally

is a completely new concept that doesn't appear anywhere in the support here.

So in order for the author to use this premise to reach this conclusion,

they have to assume something about exercising muscles equally.

And the thing that's missing is the idea that

if you want balanced muscle development,

then it's required or important to exercise muscles equally.

What's happening here is just the standard form of

if you have a premise that says if A then B,

and then a conclusion that says therefore A arrows to C,

the thing that's missing is adding B goes to C.

That's how we can identify that this part is missing.

That if you want balanced muscle development,

it's important to exercise your muscles equally.

Or the contrapositive of that, which would be

if you don't exercise your muscles equally,

then that won't lead to balanced muscle development.

Now at this point, for the purpose of this explanation,

What B says is exercising the muscles on opposite sides of the spine unequally

tends to lead to unbalanced muscle development.

And that's just working off of the contrapositive of this idea.

If you don't exercise your muscles equally,

then that tends to not lead to balanced muscle development.

Now you can also use the negation technique here

to understand why B is necessary.

Because if you negate B, that's going to undermine

the link between this premise and this conclusion.

And here's how.

The negation of B is exercising the muscles on opposite sides of the spine unequally

does not tend to lead to unbalanced muscle development.

In other words, if you exercise your muscles on opposite sides unequally,

you can still be just as likely to have balanced muscle development.

That's the negation of B.

And if that were the case, then why would having a healthy back

require exercising the muscles equally?

If you could exercise the muscles unequally

and be just as likely to have balanced muscle development,

then the fact we need balanced muscle development

doesn't constitute a reason we need to exercise the muscles equally.

Or to be more precise, it doesn't constitute a reason

that it's important to exercise muscles equally.

Why would we have to do this if not doing it

doesn't undermine our chances of balanced muscle development?

That's how the negation of B hurts this argument.

Now at its core, if you just focus on this part of the argument,

you might recognize that B isn't that unusual of an assumption.

And by that, I just mean that we'll have encountered many problems

where the missing piece is just the idea of B going to C.

The assumption is that B here goes to C. That's the missing piece.

But the problem is there's another piece of the argument here, the premise,

and there are assumptions that are associated with the premise to the intermediate conclusion

and that can really throw us off when we look at the other answer choices.

So let me go ahead and break down what's going on from the premise to the intermediate conclusion,

but I will caution you that in a time situation,

if I'm recognizing the logic of B, I'm just picking this and moving on.

There's no reason in a time situation we would want to dig into the premise to intermediate conclusion

if we've already spotted this gap over here.

So let's go ahead and diagram the premise now

to see if we can spot gaps between the premise and the intermediate conclusion.

The premise says muscles on opposite sides of the spine

must pull equally in opposing directions

to keep the back in proper alignment and protect the spine.

So the thing that must happen is necessary.

You need the muscles to pull equally in opposing direction

in order to keep the back in proper alignment and protect the spine.

So I'm just going to simplify that to protect the spine,

even though it's technically two different ideas.

Because this is necessary to protect the spine,

the author reaches this intermediate conclusion

that therefore in order to have a healthy back, we need balanced muscle development.

Now what I'm about to do next is going to be pretty advanced,

so if it doesn't make sense to you right now, that's totally fine.

The issue that I'm going to explore, it just doesn't happen that often,

and so you don't really need to concern yourself with it

until you're like really good at logical reasoning

and trying to pick up every single point in the section.

Let me off to the side here, give you an example argument,

and then see how that argument might help you understand the structure

of what's happening in the premise to the intermediate conclusion here.

Let's say I have the premise that all apples are fruit.

So if apple, then fruit.

And based on that, I want to reach the conclusion,

therefore if something is an apple, it must be healthy.

What's missing from this argument over here?

Well, you might recognize that the missing piece is if fruit, then healthy.

This is what's required in order for me to get from apple

and go all the way to healthy based on the fact that apples are fruit.

Now let me go ahead and change this up a little bit.

We'll still stick with the premise that if apple, then fruit,

but now I'm going to change the conclusion.

The conclusion will say, therefore everything in my refrigerator,

and so I'll just do, if in my fridge, then it is a fruit.

What's missing from this argument?

Why does the author here think that the fact all apples are fruit

proves that everything in my fridge is a fruit?

Well, the missing piece is the assumption that everything in my fridge is an apple.

Here the argument's assuming, if it's in my fridge, then that means it's an apple,

and that's why the author thinks that everything in my fridge is a fruit.

But now let me change up the argument one more time.

I'm still going to have the premise, if apple, then fruit,

but this time the conclusion will say,

therefore everything in my fridge is healthy.

This is the kind of argument that just trips so many people up

because it contains multiple assumptions now.

But structurally, what's happening is that I've just combined

the first two argument examples that I gave you into one.

Remember, in the first argument, the conclusion was, therefore all apples are healthy.

And in that one, the missing piece was, if fruit, then healthy.

In the second argument, the conclusion was, everything in my fridge is a fruit.

And the missing piece of that one was the assumption that everything in the fridge was an apple.

This argument down here, where the conclusion is, if fridge, then healthy,

is just making both of those assumptions.

It is assuming everything in the fridge is an apple,

and then it is also assuming that everything that is a fruit is healthy.

That's why the author thinks the fact all apples are fruit

proves that everything in my fridge is healthy.

So what's happening in the premise-to-intermediate-conclusion jump in this argument

is structurally the same.

The author is assuming that in order to have a healthy back,

you have to protect the spine and keep the back in proper alignment.

That's one of the assumptions of the argument.

But another assumption of the argument is that if you want your muscles to pull equally in opposing directions,

that requires having balanced muscle development.

Now it's possible that when you read this argument,

you basically just treated this as the same thing as that.

And if that's the case, you probably would have been less confused by some of these answers.

But I think, technically, these are different things.

The idea of muscles pulling equally in opposite directions

is not exactly the same as muscle development and it being balanced.

So there is this assumption here.

So ultimately, this argument here,

if you consider everything, including the premise and the intermediate conclusion,

was making three assumptions.

The assumption that in order to have a healthy back, you have to protect the spine.

In order for the muscles to pull equally in opposing directions, you have to have balanced muscle development.

And then it was also making the assumption that in order to have balanced muscle development,

you have to exercise your muscles equally.

So now let's go ahead and examine the wrong answers and why they're wrong.

So let's take a look at A. Is this necessary to the argument?

will be enough to keep the back in proper alignment.

So remember, the idea of keeping the back in proper alignment

was something that I just mushed together with protecting the spine.

And so keeping the back in proper alignment is this concept right here.

Does the argument have to assume that having the muscles on opposite sides be equally well-developed

will be enough, or in other words, is sufficient to keep the back in proper alignment?

Well, no, that's not necessary because that's just trying to take this concept here

or maybe this concept or some combination of those two concepts

and then trying to go backwards on the relationship.

What the argument is saying is keeping the back in proper alignment

requires that the muscles pull equally in opposite directions,

which in turn requires balanced muscle development.

But that does not mean that balanced muscle development or equal muscle development

is going to be sufficient for protecting the spine.

All we know is that it's necessary.

And so that's why A is wrong.

Now you can also negate this and say,

well, what if muscles on opposite sides of the spine being equally well-developed

will not be enough to keep the back in proper alignment?

That doesn't hurt the argument because even if it's not enough,

it could still be required.

So that's why A is wrong.

provided that one exercises the muscles on opposite sides of the spine equally,

one will have a generally healthy back.

Now the phrase provided that here is introducing a sufficient condition.

What it means is, if you do this,

if you exercise the muscles on opposite sides equally,

then you will have a generally healthy back.

But you might notice that this is actually just

reversing the direction of this conclusion here.

The conclusion was saying, if you want a healthy back,

then it's important to exercise muscles equally.

But that doesn't mean that exercising muscles equally on both sides

is sufficient to guarantee a healthy back.

And by the way, the word generally here

is not making this less than sufficiency.

And by that I mean, don't read this as saying,

provided that you exercise the muscles on opposite sides equally,

you'll probably have a healthy back.

That's not the way the word generally is being used here.

What this is saying is,

if you exercise the muscles on opposite sides of the spine equally,

then you will have, in general, a healthy back.

It is saying that you will have a healthy back,

but it's just specifying that we just mean healthy in general.

We don't necessarily mean that each of the specific parts of the back are healthy.

So the word generally does not save this answer from being wrong.

What C is saying is still that if you do this,

that is going to lead to a healthy back, a generally healthy back.

And that's just reversing the direction of the conclusion.

So that's why answer choice C is wrong.

Now by the way, you could also negate this to understand why it's not necessary.

The negation is, even if you exercise the muscles on opposite sides of the spine equally,

you will not necessarily have a generally healthy back.

But that doesn't hurt the argument because the argument wasn't saying

that if you exercise, you will have a healthy back.

So even if you won't automatically have a healthy back,

this could still be necessary in order to have a healthy back.

That's perhaps another way to think about why C is not required for this argument.

one's back will be irreparably damaged.

Now this is not necessary because we don't need unequal exercise to lead to irreparable damage.

And by irreparable, that means it's damage that cannot be repaired.

Although the argument does have to assume in order to have balanced muscle development,

you need to exercise the muscles equally,

that doesn't mean if you don't exercise the muscles equally,

there will be some damage that is impossible to heal from.

All that the author thinks is that if you don't exercise the muscles equally,

that tends not to lead to balanced muscle development.

But maybe imbalanced muscle development is something you could repair.

So it goes too far to say that the author has to assume that something can't be repaired.

to ensure that the muscles on opposite sides of the spine keep the back in proper alignment.

But the most glaring thing about E that makes it not necessary is this idea of daily exercise.

Nothing in the argument talked about how regularly or how often we need to exercise.

Maybe we can have balanced muscle development with like weekly exercise or monthly exercise.

There's no reason why the author thinks it has to be daily or that one should exercise daily.

Maybe the author just thinks it's okay to exercise a few times every year,

it's just that when you do it, you need to make sure that you're exercising both sides equally

if you want a healthy back.

That's all that the author has to assume.

So that's why E is not necessary.

Now I want to emphasize again, in a timed situation,

I'm really just picking up on this jump over here

and I'm being very focused on the intermediate conclusion to main conclusion

because if you're able to spot that gap,

there's a good chance that the correct answer is going to relate to that gap.

But for the purpose of the explanation, I went into a lot more detail regarding the premise here

just because I view it as my obligation to help you get a full, complete understanding of what's going on in this problem.

You probably didn't need to understand this to solve this problem accurately and quickly,

but on some of the hardest problems out there,

understanding what happened with the premise to the intermediate conclusion can be very useful.