Biconditionals

LSATHopeful-2

Hey guys quick question, is /J <-> L the same thing as J <-> /L?

Could you explain why they are/are not the same please!

Thanks

DumbHollywoodActor

Yes. that’s true.

I like JY’s approach:

For A<--->/B or /A <--> B or /B <--> A or B<-->/A, A and B are always apart.

For A <--> B or B<--> A, A and B are always together.

That tends to keep things clear for me.

M.Yanka106

I think one is the contrapositive of the other. As described in the comment above, it conveys the idea that the 2 pieces are always apart. Here is how:

(1) /J ----> L = /L ------> J (2) (either or)

(3) J ------>/L = L ------> /J (4) (not both)

If you look at representations (1) and (4), you will see that the arrow is going back and forth (so to speak). Same for (2) and (3). Thus, if you find two separate statements or a statement with "either or.... not both" in it, you can set it up this way and conclude that the pieces are forever apart.

Hope that helps. If I am wrong, I am sure @DumbHollywoodActor will let us both know.

wilderness

Yes.

/J<->L breaks down into two conditionals:

(1) /J --> L
(2) L --> /J

Let's take the contrapositives of each.

(1b) /L --> J
(2b) J --> /L

We can combine (1b) and (2b) to form the following biconditional:

(2) /L <-> J , or as you put it, J <-> /L

We can do this because contrapositives are logically equivalent propositions.