# Truth- Functionally Equivalent

Use truth tables to test which of the following propositional forms are truth- functionally equivalent to each other:

1. ~(p q)

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2. ~(~p ~q)

3. ~p & ~q

4. p & q

Use truth tables to determine whether the expressions in each of the following pairs are truth-functionally equivalent:

1. “p” and “p & p” 9. “~(p q)” and “~p q”

2. “p” and “p p” 10. “~(p q)” and “~p & ~q”

3. “p ~p” and “~(p & ~p)” 11. “~~(p q)” and “~~p & ~~q”

4. “p” and “p & (q ~q)“ 12. “~(p & q)” and “~p q”

5. “p” and “p & (q & ~q)” 13. “~~(p & q)” and “~~p ~~q”

6. “p” and “p (q & ~q)” 14. “~~p ~~q” and “~(~p & ~q)”

7. “p & (q r)” and “p (q & r)” 15. “~~p & ~~q” and “~(~p ~q)”

8. “p & (q & r)” and “(p & q) & r” 16. “p & ~~q” and “~~p & q”