NIELIT 2016 MAR Scientist C - Section C: 25

Question

 

Which of the following is FALSE?

$Read\ \wedge as\ AND, \vee\ as\ OR, \sim as\ NOT, \rightarrow$ as one way implication and $\leftrightarrow$ as two way implication?

• A. $((x\rightarrow y)\wedge x)\rightarrow y$ 
• B. $((\sim x\rightarrow y)\wedge (\sim x\wedge \sim y))\rightarrow x$
• C. $(x\rightarrow (x\vee y))$
• D. $((x\vee y)\leftrightarrow (\sim x\vee \sim y))$

Comments

In this first three are tautology and in last option I am getting truth values as "F T  T F".
May be there is something missing either in the question or in the options.

Answer 1

OPTION D

https://gateoverflow.in/2732/gate1996-2-3

Answer 2

TAKE OPTION A

((x→y)∧x)→y((x→y)∧x)→y

Truth value :  T ,T ,T ,T

Take option B :

((∼x→y)∧(∼x∧∼y))→x

Truth value :T ,T, T,T

Take option C

 

(x→(x∨y))

Truth value : T ,T,T ,T

taking option d

 

((x∨y)↔(∼x∨∼y))

Truth value :

F , T, T, F

Hence option d is correct .