The negation of the Boolean expression \sim s\vee (\sim r\wedge s) 

is equivalent to :

  • Option 1)

    \sim s\wedge\sim r

  • Option 2)

    r

  • Option 3)

    s\vee r

  • Option 4)

    s\wedge r

 

Answers (1)

negation of the Boolean expression \sim s\vee (\sim r\wedge s) = \sim(\sim s)\wedge\sim (\sim r\wedge s)

Applying De morgans law,

\sim(A\vee B)=\sim A \: \wedge \sim B

= s\wedge (\sim(\sim r)\vee (\sim s))

=(s\wedge r)\vee(s\wedge \sim s)

Using double negation law and distributive law 

A\wedge (B\vee C)=(A\wedge B)\vee(A\wedge C)

=> (S\wedge r)\vee F

Contradiction (A\wedge \sim A)= F

=> (S\wedge r)

So, option (4) is correct.


Option 1)

\sim s\wedge\sim r

Option 2)

r

Option 3)

s\vee r

Option 4)

s\wedge r

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