The contrapositive of the statement "If it is raining, then I will not come", is
The contrapositive of the statement "If it is raining, then I will not come", is
- [JEE MAIN 2015]
- A
If I will not come, then it is raining.
- B
If I will not come, then it is not raining.
- C
If I will come, then it is raining.
- D
If I will come, then it is not raining.
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The number of choices of $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$, such that $( p \Delta q ) \Rightarrow(( p \Delta \sim q ) \vee((\sim p ) \Delta q ))$ is a tautology, is
The number of choices of $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$, such that $( p \Delta q ) \Rightarrow(( p \Delta \sim q ) \vee((\sim p ) \Delta q ))$ is a tautology, is
- [JEE MAIN 2022]
Suppose $p, q, r$ are positive rational numbers such that $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is also rational. Then
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- [KVPY 2020]
Negation of the Boolean statement $( p \vee q ) \Rightarrow((\sim r ) \vee p )$ is equivalent to
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If $p$ : It rains today, $q$ : I go to school, $r$ : I shall meet any friends and $s$ : I shall go for a movie, then which of the following is the proposition : If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.
If $p$ : It rains today, $q$ : I go to school, $r$ : I shall meet any friends and $s$ : I shall go for a movie, then which of the following is the proposition : If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.
The statement $(\mathrm{p} \wedge(\mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r})) \rightarrow \mathrm{r}$ is :
The statement $(\mathrm{p} \wedge(\mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r})) \rightarrow \mathrm{r}$ is :
- [JEE MAIN 2021]