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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.

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