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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?

  1. $((x\rightarrow y)\wedge x)\rightarrow y$ 
  2. $((\sim x\rightarrow y)\wedge (\sim x\wedge \sim y))\rightarrow x$
  3. $(x\rightarrow (x\vee y))$
  4. $((x\vee y)\leftrightarrow (\sim x\vee \sim y))$
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2 Answers

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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 .
Answer:

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