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Mathematical Reasoning
medium
$(p\; \wedge \sim q) \wedge (\sim p \vee q)$ is
A
A contradiction
B
A tautology
C
Either $(a)$ or $(b)$
D
Neither $(a)$ nor $(b)$
Solution
(a) Clearly, $(p\; \wedge \sim q) \wedge (p\; \vee \sim q)$ is a contradiction.
|
$p$ |
$q$ |
$~p$ |
$~q$ |
$p \wedge ~q$ |
$~p \vee q$ |
$(p \wedge ~q) \wedge (~p \vee q)$ |
|
$T$ |
$T$ |
$F$ |
$F$ |
$F$ |
$T$ |
$F$ |
|
$T$ |
$F$ |
$F$ |
$T$ |
$T$ |
$F$ |
$F$ |
|
$F$ |
$T$ |
$T$ |
$F$ |
$F$ |
$T$ |
$F$ |
|
$F$ |
$F$ |
$T$ |
$T$ |
$F$ |
$T$ |
$F$ |
Standard 11
Mathematics
