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Standard XII

Mathematics

Union of Sets

If a is false...

Question

If $a$ is false, $b$ is true and $c$ is false, then which of the following is false?

(a \land b) \Rightarrow c

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a \Rightarrow\sim (b \land c)

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((a \land b) \lor c) \Rightarrow a

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\sim (a \Rightarrow b) \land (\sim c \Rightarrow b)

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Solution

The correct option is D $\sim (a \Rightarrow b) \land (\sim c \Rightarrow b)$
$A)$
$\begin{matrix} a & b & c & a \land b & (a \land b) \Rightarrow c F & T & F & F & T \end{matrix}$

$B)$
$\begin{matrix} a & b & c & b \land c & \sim (b \land c) & a \Rightarrow\sim (b \land c) F & T & F & F & T & T \end{matrix}$

$C)$
$\begin{matrix} a & b & c & a \land b & (a \land b) \lor c & ((a \land b) \lor c) \Rightarrow a F & T & F & F & F & T \end{matrix}$

$D)$
$\begin{matrix} a & b & c & a \Rightarrow b & \sim (a \Rightarrow b) & \sim c & \sim c \Rightarrow b & \sim (a \Rightarrow b) \land (\sim c \Rightarrow b) F & T & F & T & F & T & T & F \end{matrix}$

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