The number of minterms in an \( n \) variable truth table is:
Show Hint
- \( n^2 \)
- \( (n-1)^2 \)
- \( 2^n \)
- \( 2^{n-1} \)
The Correct Option is C
Solution and Explanation
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).
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