Question

The dual of the statement `Mangoes are delicious but expensive' is

• A. Mangoes are delicious or Mangoes are not expensive.
• B. Mangoes are not delicious and Mangoes are not expensive.
• C. Mangoes are delicious or Mangoes are expensive.
• D. Mangoes are delicious and Mangoes are expensive.

Hint:

To find the dual of a logical statement, replace AND by OR and OR by AND, without changing the propositions.

Answer 1

The Correct Option is C

Step 1: Interpreting the given statement.
The statement “Mangoes are delicious but expensive” can be written logically as: \[ p \land q \] where $p$: Mangoes are delicious, and $q$: Mangoes are expensive.
Step 2: Understanding the concept of duality.
The dual of a statement is obtained by interchanging logical AND ($\land$) with logical OR ($\lor$), without negating the propositions.
Step 3: Writing the dual statement.
The dual of $p \land q$ is \[ p \lor q \] That is, “Mangoes are delicious or Mangoes are expensive.”
Step 4: Conclusion.
Hence, the correct dual statement is option (C).