For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
The school is closed if it is a holiday or a Sunday.
The school is closed if it is a holiday or a Sunday.
(A) In this statement,the "Or" is inclusive. The school remains closed if it is a holiday,if it is a Sunday,or if it is both (e.g.,a Sunday that is also a holiday). Since the condition is satisfied in all these cases,it is an inclusive "Or".
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Consider the following statements:
$P :$ Suman is brilliant
$Q :$ Suman is rich
$R :$ Suman is honest
The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as:
$P :$ Suman is brilliant
$Q :$ Suman is rich
$R :$ Suman is honest
The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as:
The negation of the statement "If $5 < 7$ and $7 > 2$,then $5 > 2$" is
Write the following statement in five different ways,conveying the same meaning.
$p:$ If a triangle is equiangular,then it is an obtuse-angled triangle.
$p:$ If a triangle is equiangular,then it is an obtuse-angled triangle.
Medium
View Solution$(p \wedge r) \Leftrightarrow (p \wedge (\sim q))$ is equivalent to $(\sim p)$ when $r$ is.
The converse of the contrapositive of the conditional $p \rightarrow \sim q$ is
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