If ab = 0,write the contrapositive of the sta | vedclass

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Question

(C) Let $p : ab = 0$,$q : a = 0$,and $r : b = 0$. The given statement is $p \Rightarrow (q \lor r)$. The contrapositive of $p \Rightarrow (q \lor r)$

Vedclass · Accepted Answer

If $(a 
eq 0 	ext{ and } b 
eq 0)$,then $ab 
eq 0$

Vedclass · Answer

(C) Let $p : ab = 0$,$q : a = 0$,and $r : b = 0$. The given statement is $p \Rightarrow (q \lor r)$. The contrapositive of $p \Rightarrow (q \lor r)$ is $\sim (q \lor r) \Rightarrow \sim p$. Using De Morgan's Law,$\sim (q \lor r) \equiv (\sim q \land \sim r)$. Thus,the contrapositive is $(\sim q \land \sim r) \Rightarrow \sim p$. Substituting the values,we get: If $(a 
eq 0 	ext{ and } b 
eq 0)$,then $ab 
eq 0$.

If $ab = 0$,write the contrapositive of the statement $(a = 0 \text{ or } b = 0)$.

Similar Questions

The correct logical equivalences from the following are:
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