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Mathematical Reasoning
hard
निम्न में से कौनसा सत्य है
A
$p \Rightarrow q \equiv \;\sim p \Rightarrow \;\sim q$
B
$\sim (p \Rightarrow \;\sim q) \equiv \;\sim p \wedge q$
C
$\sim (\sim p \Rightarrow \,\sim q) \equiv \sim p \wedge q$
D
$\sim (p \Leftrightarrow q) \equiv [\sim (p \Rightarrow q) \wedge \sim (q \Rightarrow p)]$
Solution
(c) $\sim (p \Rightarrow q) \equiv p\; \wedge \sim q$
$\sim (\sim p \Rightarrow \;\sim q) \equiv \;\sim p\; \wedge \sim (\sim q) \equiv \;\sim p \wedge q$
अत: $\sim (\sim p \Rightarrow \;\sim q) \equiv \;\sim p \wedge q$.
Standard 11
Mathematics
