Question

The dual of the following statement "Reena is healthy and Meena is beautiful" is

• A. Reena is not beaufiful and Meena is not healthy.
• B. Reena is not beautiful or Meena is not healthy.
• C. Reena is not healthy or Meena is not beautiful.
• D. None of these.

Answer 1

Answer: (C)

Reena is not healthy or Meena is not beautiful.

Let $p$ denote the statement "Reena is healthy"

and $q$ denote the statement "Meena is beautiful"

Now the given statement is $p\wedge q$

Now the Dual of this statement will be obtained by replacing $\vee$ by

$\wedge$ and $\wedge$ by $\vee$ and inversing the true value of the statement.

So the Dual of $p\wedge q$ will be $\sim p\vee \sim q$

The statement $\sim p$ will be "Reena is not healthy"

The statement $\sim q$ will be "Meena is not beautiful"

So the dual statement will be $\sim p\vee \sim q$ or "Reena is not healthy or Meena is not beautiful."