Is a clause "A" a tautology if and just if it contains both the atoms p and ¬p at the same time?

Asked Sep 17 '17 at 18:59

Active Sep 17 '17 at 20:01

Viewed 47 times

I'm just starting boolean algebra, and I'm kind of stuck here.

I know $A=(p \text{ or } ¬p)$ is a tautology, and what I've tried to do is to find an example of a tautological clause that does not include $p$ or $¬p$ at the same time, without success.

Any help?

edited Sep 17 '17 at 20:01

Michael Hardy

asked Sep 17 '17 at 18:59

Chus

Every tautology is reducible to this form, where in general $p$ may be a non-atomic formula. – Myridium Sep 17 '17 at 19:05
What is your opinion of the form $p\to (q\to p) $? – hardmath Sep 17 '17 at 19:13
$p\wedge\neg p$ contains the two things you say and it is not a tautulogy. – Mariano Suárez-Álvarez Sep 17 '17 at 19:15
Perhaps you need to define "clause", so people won't attempt answers with formulas other than clauses. – GEdgar Sep 17 '17 at 19:31

Is a clause "A" a tautology if and just if it contains both the atoms p and ¬p at the same time?

0 Answers0