Conditional Logic Question on MLSAT LR 'Drill It' re '

[inline]

3rd edition of MLSAT LR on pp 336. I am completely missing the jump between "˜if’ and "˜only if’ in the drill it section;

For example q1 asks; "˜if Janet goes to the party then Bill goes to the party’ (choose all logically equivalent answers)

(a) If Janet does not go to the party then Bill does not go.
(b) Janet goes to the party only if Bill goes.
(c) Bill goes to the party only if Janet goes
(d) If Bill does not go to the party then Janet does not go.


I totally get that "if J->B" thus answer D is clearly correct since -B -> -J

What I *do not* get is why (B) is also correct....the statement "˜if Janet goes to the party then Bill goes to the party’ did not include an ONLY IF anywhere...so I’m just missing the equivalent logic somehow.

Can someone give me a gentle SHOVE in the right direction?

[tommywallach]

Hey Inline,

I will eat pizza only if you ride the bicycle.

P --> B

See why? Because the only way the pizza will happen is if the bicycle happens/happened. So if you see pizza, you know the bicycle was ridden. It's no different from:

If I eat pizza then you will ride the bicycle.

P --> B

Weird, right?

Now if it said "I will eat pizza if and only if you ride the bicycle," that would be:

P <--> B

Hope that helps!

-t