Question

Write the dual of following:
$(p\wedge c)\wedge (q\wedge c)$
where $t$ stands for tautology and $c$ stands for contradiction

• A. $p\wedge q$
• B. $c$
• C. $t$
• D. $p\vee q$

Answer 1

Answer: (C)

$t$

$[p\wedge q]\wedge [q\wedge c]$

$A\wedge B\to$ True if both A and B are true.

$[p\wedge q]\to$ c is false.

$\Rightarrow p\wedge c\to$ false.

$q\wedge c\to$ c is false.

$\Rightarrow q\wedge c\to$ false.

$[p\wedge q]\wedge [q\wedge c]$

$F\wedge F$.

Hence, correct answer is $t$.