Describe how to prove a biconditional statement P if Q Then

Describe how to prove a biconditional statement P if Q. Then outline how you would prove: A = B A Times B = B Times A.

Solution

A biconditional statement P iff Q means P is true if and only if Q is true.

For this we need to first assume P is true and prove Q is true

Then we assume Q is true and then prove that P is true

For the given problem. We first assume

A=B

Let, (x,y) be any element in AxB

Hence, x is in A and y is in B but A=B so x is in B and y is in A also

So,(x,y) is in BxA

Let, (x,y) be any element in BxA

So, x is in B and y is in A

Since, A=B

x is in A and y is in B

So,(x,y) is in AxB

Hence, AxB=BxA

Now assume,

AxB=BxA

Let, (x,y) be any element in AxB

Hence, x is in A and y is in B

But, AxB=BxA

so, x is in B and y is in A

Hence, B=A