Question

If a statement has n variables, how many rows are in the truth table?

a) 2^n
b) n^2
c) n
d) 2 * n

Answer 1

The number of rows in a truth table for a statement with n variables is 2 to the power of n (2^n), reflecting all possible combinations of truth values for the variables.

Step-by-step explanation:

When creating a truth table for a statement with n variables, one must consider all possible combinations of truth values for each variable. Since each variable can take on two values (true or false), the total number of combinations is the product of the number of possibilities for each variable. This calculation is performed as 2 to the power of n (2n).

Therefore, if a statement has n variables, the number of rows in the truth table is 2n.

For example, with 2 variables, there would be 22 = 4 rows, and with 3 variables, there would be 23 = 8 rows. This exponential growth shows why truth tables become quite large as the number of variables increases.