Consider 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
- A$(A \wedge C) \wedge (\sim B)$
- B$(\sim B) \wedge (A \wedge C)$
- C$B \rightarrow ((\sim A) \vee (\sim C))$
- D$B \rightarrow (A \wedge C)$
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The negation of $p \wedge (q \rightarrow r)$ is
Let $p, q, r$ denote arbitrary statements. Then the logical equivalent of the statement $p \Rightarrow (q \vee r)$ is
DifficultJEE MAIN 2014
View SolutionIf $p \rightarrow (q \vee r)$ is false,then what are the truth values of $p, q, r$ respectively?
Easy
View SolutionWhich of the following statements is correct?
$(a)$ $S_1: (p \wedge q) \equiv \sim(p \rightarrow \sim q)$
$(b)$ $S_2: (p \wedge q) \wedge (\sim p \vee \sim q)$ is a tautology
$(c)$ $S_3: [p \wedge (p$ $\rightarrow \sim q)]$ $\rightarrow q$ is a contradiction
$(d)$ $S_4: p$ $\rightarrow (q$ $\rightarrow p)$ is a contingency
$(a)$ $S_1: (p \wedge q) \equiv \sim(p \rightarrow \sim q)$
$(b)$ $S_2: (p \wedge q) \wedge (\sim p \vee \sim q)$ is a tautology
$(c)$ $S_3: [p \wedge (p$ $\rightarrow \sim q)]$ $\rightarrow q$ is a contradiction
$(d)$ $S_4: p$ $\rightarrow (q$ $\rightarrow p)$ is a contingency
$(p \wedge \sim q) \wedge (\sim p \wedge q)$ is
Medium
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