NIELIT 2017 July Scientist B (CS) - Section B: 16

Question

Which of the following propositions is tautology?

• A. $(p\lor q)\to q$
• B. $p\lor (q\to p)$
• C. $p\lor (p\to q)$
• D. Both (B) and (C)

Comments

Option $(C)$

$p\vee (p\rightarrow q) \equiv p\vee \neg p \vee q \equiv T \vee q \equiv T$

Answer 1

ANS :C 

 

p∨(p→q)

p	q	P->Q	p∨(P->Q)
T	T	T	T
T	F	F	T
F	T	T	T
F	F	T	T

 

Answer 2

To prove that the given wff isn't a tautology we need to get False value. For A -> B, we need to get T -> F case.

A.  q=F, p v q need to be T, q is F, p we can set as T. T v F = T , so T -> F. Hence not a tautology.

B. p = F, q=T. p v (q -> p) => F v (T -> F) => F

C. p = F, p -> q need to be false. But as p is T, we can never get it at F. Suppose we set p = T, then expression is always T.

So C is correct.

Answer 3

A tautology is a proposition that is always true for every value of its propositional values.

Note: we can solve such types of questions by either using the truth table method or applying logical equivalences rules. Here I use the truth table method.

Option 1) : not tautology.

$p$	$q$	$p\lor q$	$(p\lor q)\to q$
T	T	T	T
T	F	T	F
F	T	T	T
F	F	F	T

Option 2): Not tautology.

$p$	$q$	$q\to p$	$p \lor (q \to p)$
T	T	T	T
T	F	T	T
F	T	F	F
F	F	T	T

option 3): it is a tautology.

$p$	$q$	$p\to q$	$p \lor(p\to q)$
T	T	T	T
T	F	F	T
F	T	T	T
F	F	T	T

Option $(C)$ is correct.