- Home
- Standard 11
- Mathematics
Mathematical Reasoning
medium
Consider the two statements :
$(\mathrm{S} 1):(\mathrm{p} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$ is a tautology
$(S2): (\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\sim \mathrm{p} \vee \mathrm{q})$ is a fallacy.
Then :
A
only $(S1)$ is true.
B
both $(S1)$ and $(S2)$ are false.
C
both $(S1)$ and $(S2)$ are true.
D
only $(S2)$ is true.
(JEE MAIN-2021)
Solution
$S_{1}:(\sim p \vee q) \vee(q \vee p)=(q \vee \sim p) \vee(q \vee p)$
$S_{1}=q \vee(\sim p \vee p)=q v t=t=$ tautology
$S_{2}:(p \wedge \sim q) \wedge(\sim p \vee q)=(p \wedge \sim q) \wedge \sim(p \wedge \sim q)=C$
$=\text { fallacy }$
Standard 11
Mathematics
