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What is the number of rows in a truth table for a well-formed formula that has n different statement letters?

publish date: 2022/06/15 09:07:00 GMT+10

volume_mute

For a single statement letter, you have two possibilities T or F

For a two statement letters formula, you have two possibilities for each one, and the permutation = 2 * 2 = 4, or 2²

For 3 letters, permutation = 2 * 2 * 2 = 2³

So for n letters formula, it will be 2ⁿ

Have a look into the below binary tree

$truth-table-tree.png$

Mathematical Structures for Computer Science, Discrete Mathematics and its Applications, seventh edition, go-math-science.com