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

2 Answers
Jul 16, 2018

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.

Jul 19, 2018

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!