The Boolean Expression (p\wedge \sim q)\vee q\vee (\sim p\wedge q) is equivalent to :

  • Option 1)

    \sim p\wedge q

     
  • Option 2)

    p\wedge q

  • Option 3)

    p\vee q

  • Option 4)

    p\: \vee \sim q

 

Answers (1)

As we learnt in 

Truth table of 'OR' operator -

-

 

 

Truth Table of "NOT" operator -

-

 

Let us make truth table for  

 

                      \left ( p\:\wedge \sim q \right )\vee q \: \vee \left ( \sim p\wedge q \right )

p q \sim q p\:\wedge \sim q \left ( \sim p\wedge q \right ) \left ( p\:\wedge \sim q \right )\vee q     \left ( p\wedge\sim q \right )\vee q \vee \left ( \sim p\wedge q \right )    
T T F F F T T
T F T T F T T
F T F F T T T
F F T F F F F

It is same as p\vee q


Option 1)

\sim p\wedge q

 

Incorrect

Option 2)

p\wedge q

Incorrect

Option 3)

p\vee q

Correct

Option 4)

p\: \vee \sim q

Incorrect

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