GATE Overflow | Mathematics | Test 1 | Question: 26

Question

Which of the following propositions is a tautology ?

• A. $(p \vee q) \to p$    
• B. $p \vee (q \to p )$
• C. $p \vee ( p \to q )$   
• D. $p \to (p \to q )$

Answer 1

Option C.

Table

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

Answer 2

C) p v (p->q)
  =p v (p'vq)
  =(p v p') v q
  =T v q
  = T

Hence  Tautology.