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Mathematical Reasoning
medium
If $p$ and $q$ are simple propositions, then $p \Rightarrow q$ is false when
A
$p$ is true and $q$ is true
B
$p$ is false and $q$ is true
C
$p$ is true and $q$ is false
D
Both $p$ and $q$ are false
Solution
(c) is false, when $p$ is true and $q$ is false.
Since $q, r$ are false $\therefore $ $q \vee r$ is false.
Since $r$ is false $\therefore $ $\sim \,r$ is true.
Since $p\; \wedge \sim \,r$ is true $\therefore $ $p$ is true.
Standard 11
Mathematics
