[MERGED] Logic question: Given a ^ b, (a v c) => d, prove...

[yhk99]

i don't think this question should be under geometry and trig but it's what we're learning in geometry, and i don't know where else to post it, so...

anyway, i don't know how to do this problem.

Given:
a ^ b
(a v c) --> d
Prove:
a ^ d

what you have to do is use the givens on a Statement/Reason chart to get to the prove, using all the laws and stuff.

just so you know, ^ means "and", v means "or" and --> if/then but if you didn't know that you probably can't help me...

 

[Mrspi]

Re: Logic question?

i don't think this question should be under geometry and trig but it's what we're learning in geometry, and i don't know where else to post it, so...

anyway, i don't know how to do this problem.

Given:
a ^ b
(a v c) --> d
Prove:
a ^ d

what you have to do is use the givens on a Statement/Reason chart to get to the prove, using all the laws and stuff.

just so you know, ^ means "and", v means "or" and --> if/then but if you didn't know that you probably can't help me...

Ok...here are your givens:

Given:

a AND b
(a OR c) --> d

You are given
a AND b, which means the statement "a AND b" must be true. An "and" statement is true if and only if both parts are true.

So you know that "a" is true, and "b" is true.

Next given says (a OR c) --> d

An "or" statement is true whenever either (or both) parts is true. We've got (a OR c) and we know that "a" is true...thus (a OR c) is true.

And since (a OR c) --> d is given, we have a true implication. An implication, or "if-then" statement is only false when the hypotheses (if part) is true, and the conclusion (then part) is false. We KNOW that (a OR c) is true. And because it is given that (a OR c) -->d is true, we also know that d must be true.


I don't know what "names" you've been given for the various logic laws. But, I'm guessing this might be an example of the Law of Detachment:

p
p-->q
therefore, q

 

[DrMike]

Re: Logic question?

a ^ b implies a
a implies a v c
a v c and (a v c) --> d together imply d
a and d together imply a ^ d