Prove the following logical Equivalences using truth tables

Idempotent:

– p ^ p = p, and

– p V p = p

Absorption:

– p V (p ^ q) = p, and

– p ^ (p Ú q) = p

Identity:

– p ^ t = p, and

– p V c = p

Negation:

– p V ~p = t, and p ^ ~p = c

Universal Bound:

– p ^ c = c, and

– p V t = t

Negations of t and c:

– ~t = c, and

– ~c = t

Note: t means tautology, c means contradiction.

This is what i have done so far please let me know if i am doing it right or if anything is wrong. Thanks

Idempotent:

p p^p pVp

0 0 0

1 1 1

Absorption:

p q p^q pv(p^q) pVq p^(pVq)

0 0 0 0 0 0

0 1 0 0 1 0

1 0 0 1 1 1

1 1 1 1 1 1

Identity:

p t c p^t pVc

0 1 0 0 0

1 1 0 1 0

Negation:

p ~p pV~p p^~p

0 1 1 0

1 0 1 0

Universal Bound:

p c t p^c pVt

0 0 1 0 1

1 0 1 0 1

Negations of t and c:

t c ~t ~c

1 0 0 1

When an expression is always 0 it is a contradiction, and when it is always 1 it is a tautology.