Contrapositive question - please assist Forum

[katie96]

Okay, maybe my mind is just numb from studying for the past few hours, and this question may seem totally stupid to some of you brilliant minds out there, but I am just not understanding this.

If G is inspected on day 3, Q is inspected on day 5.

Via the contrapositive, if Q is NOT inspected on day 5, then G is not inspected on day 3. But that doesn't make sense to me because it stands to reason that Q could still be inspected on day 5 even if G is inspected on some day other than 3?

[NZA]

I don't see how you're confused. Everything you've said makes sense.

If P, then Q.

If not Q, then not P.

If Q...maybe P? Maybe not.

[bhan87]

Okay, maybe my mind is just numb from studying for the past few hours, and this question may seem totally stupid to some of you brilliant minds out there, but I am just not understanding this.

If G is inspected on day 3, Q is inspected on day 5.

Via the contrapositive, if Q is NOT inspected on day 5, then G is not inspected on day 3. But that doesn't make sense to me because it stands to reason that Q could still be inspected on day 5 even if G is inspected on some day other than 3?

You are correct. What you've pointed out is a mistaken reversal. The only situation Q triggers something is if he's not on day 5. If he is on day 5, then there are no rules that have to apply so G could be on 3 or any other spot.

[sunynp]

If you need an in-depth explanation, you might try asking in this thread:3 180s and I'm taking your LSAT questions . He seems to be a genuine guy and his explanations are pretty thorough.

I would help, but I don't know the answer.

[notaznguy]

Okay, maybe my mind is just numb from studying for the past few hours, and this question may seem totally stupid to some of you brilliant minds out there, but I am just not understanding this.

If G is inspected on day 3, Q is inspected on day 5.

Via the contrapositive, if Q is NOT inspected on day 5, then G is not inspected on day 3. But that doesn't make sense to me because it stands to reason that Q could still be inspected on day 5 even if G is inspected on some day other than 3?

Valid: G3 --> Q5
**Remember that G3 is sufficient to say that Q5 will happen and that Q5 is necessary in order for G3 to happen. This DOESN'T MEAN that G3 HAS TO HAPPEN if Q5 occurred. But, it does mean if we know first that G is inspected on the 3rd day, we automatically know for a fact that Q is inspected on the 5th day.

However, if we know first that Q was inspected on the 5th day, we cannot assume that G was also inspected on the 3rd day. That would be the Mistaken Reversal. If Q is inspected on the 5th day, then G has the possibility of being inspected on the 3rd day, but there is no obligation for G to be inspected on the 3rd day.

Contrapositive: - Q5 --> - G3
**For the contrapositive, we know that if Q is not inspected on the 5th day, we can safely assume for a fact that G was also not inspected on the 3rd day. However, we can't expect that if G was no inspected the 3rd day, then Q was not inspected the 5th day. Again, that's a Mistaken Reversal. Knowing that Q is not inspected the 5th day is sufficient for us to conclude that G was not inspected the 3rd day. However, knowing that G was not inspected the 3rd day is only necessary for us to know that Q has the possibility of not being inspected on the 5th day.

For all we know, G could be inspected 4th (which is - G3), and Q can still be inspected on the 5th. We only know that G can never be inspected on the 3rd day if Q is not inspected on the 5th day.



Think of it like this. Necessary conditions can happen by themselves all the time. They don't need to obey any conditions and they can simply occur without triggering anything. Sufficient conditions, however, always have to trigger a necessary condition.

For example, "If it is an Apple, then it is a fruit."

I can safely conclude, "I have a fruit! and it doesn't have to be an apple! It could be a watermelon, or an orange, or a banana!"
However, I can NOT conclude, "I have a fruit, and it MUST be an apple..." Does it HAVE to be an apple? No.
But if I say, "I have an apple, so it MUST be a fruit," then that is VALID.

[tyro]

If you need an in-depth explanation, you might try asking in this thread:3 180s and I'm taking your LSAT questions . He seems to be a genuine guy and his explanations are pretty thorough.

I would help, but I don't know the answer.

Are you trying to make up for what you said on the first page of that thread?

[katie96]

Okay, maybe my mind is just numb from studying for the past few hours, and this question may seem totally stupid to some of you brilliant minds out there, but I am just not understanding this.

If G is inspected on day 3, Q is inspected on day 5.

Via the contrapositive, if Q is NOT inspected on day 5, then G is not inspected on day 3. But that doesn't make sense to me because it stands to reason that Q could still be inspected on day 5 even if G is inspected on some day other than 3?

Valid: G3 --> Q5
**Remember that G3 is sufficient to say that Q5 will happen and that Q5 is necessary in order for G3 to happen. This DOESN'T MEAN that G3 HAS TO HAPPEN if Q5 occurred. But, it does mean if we know first that G is inspected on the 3rd day, we automatically know for a fact that Q is inspected on the 5th day.

However, if we know first that Q was inspected on the 5th day, we cannot assume that G was also inspected on the 3rd day. That would be the Mistaken Reversal. If Q is inspected on the 5th day, then G has the possibility of being inspected on the 3rd day, but there is no obligation for G to be inspected on the 3rd day.

Contrapositive: - Q5 --> - G3
**For the contrapositive, we know that if Q is not inspected on the 5th day, we can safely assume for a fact that G was also not inspected on the 3rd day. However, we can't expect that if G was no inspected the 3rd day, then Q was not inspected the 5th day. Again, that's a Mistaken Reversal. Knowing that Q is not inspected the 5th day is sufficient for us to conclude that G was not inspected the 3rd day. However, knowing that G was not inspected the 3rd day is only necessary for us to know that Q has the possibility of not being inspected on the 5th day.

For all we know, G could be inspected 4th (which is - G3), and Q can still be inspected on the 5th. We only know that G can never be inspected on the 3rd day if Q is not inspected on the 5th day.



Think of it like this. Necessary conditions can happen by themselves all the time. They don't need to obey any conditions and they can simply occur without triggering anything. Sufficient conditions, however, always have to trigger a necessary condition.

For example, "If it is an Apple, then it is a fruit."

I can safely conclude, "I have a fruit! and it doesn't have to be an apple! It could be a watermelon, or an orange, or a banana!"
However, I can NOT conclude, "I have a fruit, and it MUST be an apple..." Does it HAVE to be an apple? No.
But if I say, "I have an apple, so it MUST be a fruit," then that is VALID.

Thanks very much for your detailed explanation!

[Helicio]

Okay, maybe my mind is just numb from studying for the past few hours, and this question may seem totally stupid to some of you brilliant minds out there, but I am just not understanding this.

If G is inspected on day 3, Q is inspected on day 5.

Via the contrapositive, if Q is NOT inspected on day 5, then G is not inspected on day 3. But that doesn't make sense to me because it stands to reason that Q could still be inspected on day 5 even if G is inspected on some day other than 3?

Here's what you need to understand: the contrapositive is essentially the same statement as the original. All the contrapositive is showing you, at its core, is that if the necessary condition does not occur (Q is NOT inspected on day 5), then the sufficient condition cannot occur (G cannot be inspected on day 3).

Real example:

The UN resolution will pass unless a member of the security council vetoes it.

Translate to conditional statement: If the UN resolution did not pass, a member of the security council vetoed it.

For the UN resolution NOT to pass, a member of the security council MUST veto it.


Thus, the contrapositive shows that when the necessary condition does not occur, the sufficient cannot occur, because the necessary condition is necessary for the sufficient condition to occur.

Contrapositive: If a member of the security council did not veto it, the UN resolution passed.

Hope that helped.

[NZA]

Okay, maybe my mind is just numb from studying for the past few hours, and this question may seem totally stupid to some of you brilliant minds out there, but I am just not understanding this.

If G is inspected on day 3, Q is inspected on day 5.

Via the contrapositive, if Q is NOT inspected on day 5, then G is not inspected on day 3. But that doesn't make sense to me because it stands to reason that Q could still be inspected on day 5 even if G is inspected on some day other than 3?

Here's what you need to understand: the contrapositive is essentially the same statement as the original. All the contrapositive is showing you, at its core, is that if the necessary condition does not occur (Q is NOT inspected on day 5), then the sufficient condition cannot occur (G cannot be inspected on day 3).

Real example:

The UN resolution will pass unless a member of the security council vetoes it.

Translate to conditional statement: If the UN resolution did not pass, a member of the security council vetoed it.

For the UN resolution NOT to pass, a member of the security council MUST veto it.


Thus, the contrapositive shows that when the necessary condition does not occur, the sufficient cannot occur, because the necessary condition is necessary for the sufficient condition to occur.

Contrapositive: If a member of the security council did not veto it, the UN resolution passed.

Hope that helped.

This.

A possibly less confusing example:

If it rains, then it is cloudy.

It is raining, therefore, it is cloudy.

It is cloudy. It may or may not be raining.

It is not cloudy, therefore, it is not raining. This is the contrapositive.

Don't try and make the contrapositive any more complicated than it is, OP. It's a simple logical relationship between subject and predicate: nothing more.