Proving Equivalence of p and (q\Rightarrowr)

[jdm900712]

\Rightarrow

Homework Statement

I'm given two statements, p and (q\Rightarrowr) and I need to prove that the two statements are equivalent. So I need to show that p \Leftrightarrow(q\Rightarrowr)

I know that p\Rightarrow(q\Rightarrowr) \Leftrightarrow (p\wedgeq)\Rightarrowr
but I don't know how I should rewrite the converse:
(q\Rightarrowr)\Rightarrowp

Homework Equations

The Attempt at a Solution

 

[jedishrfu]

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.

 

[Mark44]

\Rightarrow

Homework Statement

I'm given two statements, p and (q\Rightarrowr) and I need to prove that the two statements are equivalent. So I need to show that p \Leftrightarrow(q\Rightarrowr)

I know that p\Rightarrow(q\Rightarrowr) \Leftrightarrow (p\wedgeq)\Rightarrowr
but I don't know how I should rewrite the converse:
(q\Rightarrowr)\Rightarrowp

Homework Equations

The Attempt at a Solution

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?

 

[Andrax]

use the truth table might work