Is this contrapositive correct? Forum

[ComatoseClown]

I wanted to clarify if my understanding of the contrapositive to this constraint is correct?

1) If Adam and Claire are selected, then Ted is selected.

Contrapositive, in words:
If Ted is not selected, then [only] Adam isn’t selected (and Claire could still be selected)
OR
If Ted is not selected, then [only] Claire isn’t selected (and Adam could still be selected)
OR
If Ted is not selected, then neither Adam nor Clarissa are selected {in other words “both Adam and Clarissa are not selected”}

(notated, respectively):
-T —> -A
OR
-T —> -C
OR
-T —> -A and -C


Is the above understanding completely correct, and particularly is what is in the parentheses completely correct?



2) For the constraint "If G is selected, then S or V is selected": Could S and V BOTH potentially be selected if G is selected; or is it limited to just one of S&V?


Thanks for taking the time to read,
cc

[Ginj]

If Adam and Claire are selected, then Ted is selected.

Contrapositive: If Ted is not selected, Adam or Claire isn't selected.

[flexityflex86]

If Adam and Claire are selected, then Ted is selected.

Contrapositive: If Ted is not selected, Adam or Claire isn't selected.

This is the correct.

You could still have one of them or have either.

You should know this if you're taking the June test....

[bport hopeful]

I thought this read "contraceptive" and came here to tell you that if you had to ask if it were correct (whatever it means for contraceptive to be correct), then it likely isnt.

[boosk]

1) If Adam and Claire are selected, then Ted is selected.
cc

If Ted is NOT selected then either Adam or Claire or both are NOT selected

[BrightLine]

If Adam and Claire are selected, then Ted is selected.

Contrapositive: If Ted is not selected, Adam or Claire isn't selected.

Right, just make sure you know that in LSAT world it means Adam or Claire or Both are not selected. It was easier for me to think of it as if Ted is not selected then it is not the case that both Adam and Claire are selected.

As far as diagramming it -T -> -(A + C)

[BrightLine]

2) For the constraint "If G is selected, then S or V is selected": Could S and V BOTH potentially be selected if G is selected; or is it limited to just one of S&V?

G -> S v V If G then either S or V or both are selected
Contrapositive -S + -V -> -G




The basic rule for contrapositive is to that you move everything from before the -> to after. And when you do so, you negate evething. So in the above example G become -G , S become -S, V becomes -V and OR( symbolized with "v") becomes AND(symbolized with +)

[ComatoseClown]

If Ted is NOT selected then either Adam or Claire or both are NOT selected

So then I assume everything I wrote in the original post is correct, right? I understand that the above quote is how the contrapositive to this is normally written -- the reason I wrote it out in longhand statements in my OP is because I wanted to know if the understanding was correct. So all the statements are correct, yes?

[AFS]

I thought this read "contraceptive" and came here to tell you that if you had to ask if it were correct (whatever it means for contraceptive to be correct), then it likely isnt.

That's what Adam and Claire were missing and that's how Ted came to be selected into the world.

[SanDiegoJake]

I wanted to clarify if my understanding of the contrapositive to this constraint is correct?

1) If Adam and Claire are selected, then Ted is selected.

Contrapositive, in words:
If Ted is not selected, then [only] Adam isn’t selected (and Claire could still be selected)
OR
If Ted is not selected, then [only] Claire isn’t selected (and Adam could still be selected)
OR
If Ted is not selected, then neither Adam nor Clarissa are selected {in other words “both Adam and Clarissa are not selected”}

(notated, respectively):
-T —> -A
OR
-T —> -C
OR
-T —> -A and -C


Is the above understanding completely correct, and particularly is what is in the parentheses completely correct?



2) For the constraint "If G is selected, then S or V is selected": Could S and V BOTH potentially be selected if G is selected; or is it limited to just one of S&V?


Thanks for taking the time to read,
cc

#1: Completely correct.
#2: Both could potentially be selected.