The correct answer is A only if B means the same thing as A implies B.

[ice109]

i don't understand why this notation is the same thing as

"A only if B"

to me "A only if B" reads that A is a consequence of B but of course it actually means the reverse.

same thing with A<->B being stated as

"A if and only if B"

to me this reads that again A is a consequence of B and is only true when B is true. I don't understand how it tells anything about B or how you read the reverse implication from it, as far as english goes.

woops i meant this for general math, wasn't looking.

 

[Hurkyl]

If we know that "A only if B", then which if these following cases are possible?

A is true and B is true.
A is true and B is false.
A is false and B is true.
A is false and B is false.

 

[ice109]

If we know that "A only if B", then which if these following cases are possible?

A is true and B is true.
A is true and B is false.
A is false and B is true.
A is false and B is false.

if i were reading and interpreting the way I'm inclined to, back wards that is, all but the second. the correct answer is of course all but the third.

the truth table i would write for the statement "A only if B" is

B is true and A is true.
B is true and A is false.
B is false and A is true.
B is false and A is false.

now i would say all but the third.

 

[Hurkyl]

if i were reading and interpreting the way I'm inclined to, back wards that is, all but the second. the correct answer is of course all but the third.

You are interpreting it correctly... "A only if B" means the same thing as "if A then B", and the case it excludes is "A is true and B is false".

Maybe you are confusing "A only if B" with "A if B"?