# A -> B

1. Nov 3, 2007

### 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.

2. Nov 3, 2007

### Hurkyl

Staff Emeritus
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.

3. Nov 3, 2007

### ice109

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.

4. Nov 3, 2007

### Hurkyl

Staff Emeritus
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"?

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