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Prove p^ (qVr) and (p^ q)V(p^r) are logically equivalent.

written 8.0 years ago by teamques10 ★ 68k

modified 2.9 years ago by pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 5 Marks

Year: May 2015

discrete mathematics

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1 Answer

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written 8.0 years ago by teamques10 ★ 68k

Consider Truth table for above expression:

p	q	r	q V r	p ^ (q v r)	p ^ q	p ^ r	(p ^ q) V (q ^ r)
T	T	T	T	T	T	T	T
T	T	F	T	T	T	T	F
T	F	T	T	T	F	T	T
T	F	F	F	F	F	F	F
F	T	T	T	F	F	F	F
F	T	F	T	F	F	F	F
F	F	T	T	F	F	F	F
F	F	F	F	F	F	F	F

Since column 5 and 8 are same.

Hence, p^ (q V r) and (p^ q) V (p ^ r) are logically equivalent

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