Prove that p→(¬q∨r)≡¬p∨(¬q∨r) using truth table.

Prove that $p \to (\neg q \lor r) \equiv \neg p \lor (\neg q \lor r)$ using truth table.

Gap-fill exercise

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LHS:

p \to (\neg q \lor r)

p	q	r	¬q	(¬q∨r)	p→(¬q∨r)
T	T	T
T	T	F
T	F	T
T	F	F
F	T	T
F	T	F
F	F	T
F	F	F

RHS:

\neg p \lor (\neg q \lor r)

p	q	r	¬q	(¬q∨r)	¬P	¬p∨(¬q∨r)
T	T	T
T	T	F
T	F	T
T	F	F
F	T	T
F	T	F
F	F	T
F	F	F

From the above tables, the last columns are . Hence

p \to (\neg q \lor r) \equiv \neg p \lor (\neg q \lor r)