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  • Let be three logical statements. Consider the compound statements <img alt="\mathrm{S}_{1}:((-p) \

Let p, q, r be three logical statements. Consider the compound statements
\mathrm{S}_{1}:((-p) \vee q) \vee((-p) \vee r)  and
{\mathrm{S}_{2}: p \rightarrow(q \vee r))}
Then, which of the following is NOT true?

Option: 1

If \mathrm{S}_{2}  is True, then \mathrm{S}_{1} is True


Option: 2

If  \mathrm{S}_{2}  is  False, then   \mathrm{S}_{1} is False


Option: 3

If \mathrm{S}_{2}  is False, then  \mathrm{S}_{1} is True


Option: 4

If \mathrm{S}_{1}  is False, then \mathrm{S}_{2} is False


Answers (1)

best_answer

\mathrm{S_{1}:\left ( \left ( \sim p \right ) \vee q\right ) \vee \left ( \left ( \sim p \right ) \vee r \right )}
       \mathrm{\equiv\left ( \sim p \right )\vee\left ( q\vee r \right ).}

\mathrm{S_{2}:p\rightarrow \left ( q\vee r \right )\equiv \sim p \vee\left ( q \vee r \right )}

\mathrm{\Rightarrow S_{1}\equiv S_{2}}

\mathrm{\Rightarrow } Option (C) is not True

Posted by

sudhir.kumar

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