Answer
The negation of the statement \[p\wedge \left( r\to \sim s \right)\] using De Morgan’s law is given as
\[\sim p\vee \sim \left( r\to \sim s \right)\].
To form the negation of a conditional statement, leave the antecedent (the first part unchanged, change the \[\text{if-then}\] connective to and) and negate the consequent (the second part). Therefore,
\[\sim \left( r\to \sim s \right)\equiv r\wedge \sim \left( \sim s \right)\].
As\[\sim \left( \sim s \right)=s\], therefore, \[r\wedge \sim \left( \sim s \right)\equiv r\wedge s\].
Thus, the negation of \[p\wedge \left( r\to \sim s \right)\] is \[\sim p\vee \left( r\wedge s \right)\].
