# Homework Help: Logic question

1. Feb 11, 2013

### jdm900712

$\Rightarrow$1. The problem statement, all variables and given/known data
I'm given two statements, p and (q$\Rightarrow$r) and I need to prove that the two statements are equivalent. So I need to show that p $\Leftrightarrow$(q$\Rightarrow$r)

I know that p$\Rightarrow$(q$\Rightarrow$r) $\Leftrightarrow$ (p$\wedge$q)$\Rightarrow$r
but I don't know how I should rewrite the converse:
(q$\Rightarrow$r)$\Rightarrow$p
2. Relevant equations

3. The attempt at a solution

2. Feb 11, 2013

### Staff: Mentor

What if you convert the p --> q to ( not (p and not q) ) and then use Boolean algebra to rework the expression and then convert back.

3. Feb 11, 2013

### Staff: Mentor

I think there is some information that is missing here. I don't see how the arbitrary statements p and (q $\Rightarrow$ r) could be equivalent.

For example, let p, q and r be the following statements:
p: x = 2
q: y = 5
r: y2 = 25

Whether p is true or false has no bearing on the implication q $\Rightarrow$ r

Are p, q, and r specific statements that aren't given in the OP?

4. Feb 11, 2013