Answer to Question #316045 in Discrete Mathematics for Pravin

Question

Prove or disprove that the two propositions in each pair are equivalent.

 (p $\bigoplus$ (q $\to$ r)), ((p $\bigoplus$ q) $\to$ (p $\bigoplus$ r))

Answer 1

$p=q=r=1:\\p\oplus \left( q\rightarrow r \right) =1\oplus 1=0\\\left( p\oplus q \right) \rightarrow \left( p\oplus r \right) =0\rightarrow 0=1\\Not\,\,equivalent$