Question

Show that the propositions p and p v (p ^ q) are logically equivalent? Must do a truth table.

Answer 1

See below

Explanation:

This definitely looks like homework, so I don't intend to do the work for you, since I am in doubt how much you actually will learn from someone else doing the work for you.

But a suggestion: Create a Venn diagram and a truth table based on that.

Answer 2

Please refer to The Explnation.

Explanation:

`"The Exp."=pvv(p^^q)`,

`=(pvvp)^^(pvvq)...[because," distributive law]"`,

`=p^^(pvvq)...[because," idempotent law]"`.

But, `p rArr p^^q`.

`:."The Exp."=p`, as desired!