Answer to Question #314708 in Discrete Mathematics for Pravin

Question

Determine whether this proposition is a tautology.

[(p → q) Ù (q → r)] → (p→ r) 

Answer 1

Let p=1,q=0,r=0. Then

$p\rightarrow q=0\\ p\rightarrow q=0\\ q\rightarrow r=1\\ (p\rightarrow q)\lor (q\rightarrow r)=1\\ ((p\rightarrow q)\lor (q\rightarrow r))\rightarrow (p\rightarrow r)=0$

The formula is not a tautology.