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Tell me? - The Boolean expressionis equivalent to : - Mathematical reasoning - JEE Main

The Boolean expression \left ( \left ( p\wedge q \right )\vee \left ( p\: \vee \sim q \right ) \right )\wedge \left ( \sim p\: \wedge \sim q \right ) is equivalent to : 

  • Option 1)

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

     

     

     

  • Option 2)

    p\wedge q

  • Option 3)

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

  • Option 4)

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

Answers (1)
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A admin

 

Negation of Conditional Statement -

\sim (p\Rightarrow q)\equiv p\wedge\sim q

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Construction of truth table -

We prepare table of rows and columns. We write variables denoting sub-statements and we write the truth value of sub statement to get compound statement.

- wherein

Figure 1

 

\left \{ \left [\left (p\wedge q\right ) \vee p \right ] \vee \left [\left(p\wedge q \right )\vee \sim q \right ] \right \}\wedge \sim(p\vee q) \\\\\Rightarrow\left \{ p\vee \left [\left (p\vee \sim q\right ) \wedge (q\vee \sim q) \right ] \right \}\wedge \sim(p\vee q) \\\\\Rightarrow \left \{ p\vee \left [p\vee \sim q\right ] \right \}\wedge \sim(p\vee q) \\\\\Rightarrow \left (p\vee \sim q\right )\wedge \sim(p\vee q) \Rightarrow \sim (p \vee q) \\\\\Rightarrow \sim p\;\wedge \sim q


Option 1)

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

 

 

 

Option 2)

p\wedge q

Option 3)

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

Option 4)

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

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