Let p, q, r denote arbitrary statements. Then the   logically   equivalent   of   the statement  p\Rightarrow \left ( q\vee r \right )

  • Option 1)

    \left ( p\vee q \right )\Rightarrow r

  • Option 2)

    \left ( p\Rightarrow q \right )\vee \left ( p\Rightarrow r \right )

  • Option 3)

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

  • Option 4)

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

 

Answers (1)

As we learnt in

If then Implications -

P implies q is denoted by p \Rightarrow q

- wherein

Symbol \Rightarrow stands for implies

 

 p\Rightarrow \left ( q\vee r \right );

" If then "

Implication is distributive in nature

So we get  p\Rightarrow \left ( q\vee r \right ) \equiv\left ( p\Rightarrow q \right )\vee \left ( p\Rightarrow r \right )

 


Option 1)

\left ( p\vee q \right )\Rightarrow r

Incorrect option

Option 2)

\left ( p\Rightarrow q \right )\vee \left ( p\Rightarrow r \right )

Correct option

Option 3)

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

Incorrect option

Option 4)

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

Incorrect option

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