Check whether "Or" used in the following compound statement is exclusive or inclusive? Write the component statements of the compound statements and use them to check whether the compound statement is true or not. Justify your answer.
$t:$ You are wet when it rains or you are in a river.
$t:$ You are wet when it rains or you are in a river.
(N/A) The "Or" used in the given statement is inclusive because it is possible that it rains and you are in the river simultaneously.
The component statements of the given statement are:
$p:$ You are wet when it rains.
$q:$ You are wet when you are in a river.
Since both component statements $p$ and $q$ can be true,the compound statement $t$ is true.
The component statements of the given statement are:
$p:$ You are wet when it rains.
$q:$ You are wet when you are in a river.
Since both component statements $p$ and $q$ can be true,the compound statement $t$ is true.
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If truth values of statements $p, q$ are true,and $r, s$ are false,then the truth values of the following statement patterns are respectively:
$a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$
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$c: (\sim p \vee q) \rightarrow(r \wedge \sim s)$
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View SolutionConsider the following statements:
$A$ : Rishi is a judge.
$B$ : Rishi is honest.
$C$ : Rishi is not arrogant.
The negation of the statement "if Rishi is a judge and he is not arrogant,then he is honest" is
$A$ : Rishi is a judge.
$B$ : Rishi is honest.
$C$ : Rishi is not arrogant.
The negation of the statement "if Rishi is a judge and he is not arrogant,then he is honest" is
The Boolean expression $\sim (p \Rightarrow (\sim q))$ is equivalent to
DifficultJEE MAIN 2019
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