Question

The number of minterms in an \( n \) variable truth table is:

• A. \( n^2 \)
• B. \( (n-1)^2 \)
• C. \( 2^n \)
• D. \( 2^{n-1} \)

Hint:

In a truth table with \( n \) variables, there are \( 2^n \) possible combinations of inputs, corresponding to \( 2^n \) minterms.

Answer 1

The Correct Option is C

Step 1: Understand the term 'minterms'.
A minterm in a truth table refers to a product term (AND operation) that represents a row in the truth table where the output is 1. In a truth table with \( n \) variables, each variable can have two states (0 or 1).

Step 2: Number of possible combinations of inputs.
The number of possible input combinations for \( n \) variables is \( 2^n \), as each variable has 2 possibilities (0 or 1). Therefore, there are \( 2^n \) rows in the truth table, each corresponding to a unique minterm.

Step 3: Conclusion.
Thus, the number of minterms in an \( n \)-variable truth table is \( 2^n \), and the correct answer is (c).