(p -> r) ^ (r -> q ) and (p -> q)

thanks

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- Mar 15th 2013, 08:44 AMAmmarAre these compound propositions logically equivalent?
(p -> r) ^ (r -> q ) and (p -> q)

thanks - Mar 15th 2013, 10:25 AMSorobanRe: Are these compound propositions logically equivalent?
Hello, Ammar!

Quote:

. . .

No, their truth-table values areidentical.*not*

- Mar 15th 2013, 10:39 AMRobertXIVRe: Are these compound propositions logically equivalent?
(p -> r) ^ (r -> q ) =/= (p -> q), However, (p -> r) ^ (r -> q) -> (p -> q).

Perhaps that helps/was what you were looking for. - Mar 15th 2013, 10:39 AMAmmarRe: Are these compound propositions logically equivalent?
Thank you soroban :)

- Mar 15th 2013, 10:48 AMAmmarRe: Are these compound propositions logically equivalent?
RobertXIV

sorry, I didn't understand. - Mar 15th 2013, 12:10 PMHallsofIvyRe: Are these compound propositions logically equivalent?
Do you understand the difference between "A is equivalent to B" and "A implies B"?

"A implies B" says that if A is true then B must be true but says nothing about what happens if A if false.

"A is equivalent to B" says that if A is true then B must be true and if A is false then B is false".

In order that (p->r)^(r->q) be true both p->r and r->q must be true. In that case, if p is true, r is true and then q is true. In other word, if p is true so is q: p->q.

But (p->r)^(r->q) is false one of p->r or r->q must be false. It might be the case, for example that p is true and r is false, so that p->r is false. That tells us nothing about whether or not q is true or false.