Question

Show that (p v q) A (p Vr)-(q vr) is a tautology.

Answer 1

The statement
`(p\lor q) \land (\\eg p \lor r)\Rightarrow (q \lor r )` is a tautology.

Explanation:

To prove this statement
`(p\lor q) \land (\\eg p \lor r)\Rightarrow (q \lor r )` is a tautology we are going to use a truth table. A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

A tautology is a formula which is true for every assignment of truth values to its simple components.

We can see from the table that the last column contains only true values. Therefore, the formula is a tautology.