Question

The dual of the statement $p\wedge [q\wedge (p\vee q)\wedge r]$ is

• A. $p\vee [q\vee (p\vee q)\vee r]$
• B. $p\vee [q\vee (p\wedge q)\wedge r]$
• C. $p\vee [q\vee (p\wedge q)\vee r]$
• D. $p\vee [q\wedge (p\wedge q)\wedge r]$

Answer 1

The correct option is C $p\vee [q\vee (p\wedge q)\vee r]$

Question :- The dual of the statement

$p\wedge [q\wedge (p\vee q)\wedge r]$ is

Solution :-

The dual of a proposition that contains

only the logical operators $\vee ,\wedge$ can be obtained

by replacing each $\vee$ by $\wedge$ and each $\wedge$ by $\vee$

So given statement

$=p\wedge [q\wedge (p\vee q)\wedge r]$

$\Rightarrow$ The dual will be $=p\vee [q\vee (p\wedge q)\vee r]$ Ans

$\to$ Required Answer c.