Questions: Introduction to truth tables with biconditional statements Complete the following truth table. Use T for true and F for false. You may add more columns, but those added columns will not be graded

Introduction to truth tables with biconditional statements

Complete the following truth table. Use T for true and F for false. You may add more columns, but those added columns will not be graded

Transcript text: Introduction to truth tables with biconditional statements Complete the following truth table. Use $T$ for true and $F$ for false. You may add more columns, but those added columns will not be graded

Solution

Solution Steps

Step 1: Understanding the Biconditional Statement

The biconditional statement $ P \leftrightarrow Q $ is true when both $ P $ and $ Q $ have the same truth value. That is, $ P \leftrightarrow Q $ is true if both $ P $ and $ Q $ are true or both are false. Otherwise, it is false.

Step 2: Evaluating Each Row

First Row ($ P = T $, $ Q = T $): Since both $ P $ and $ Q $ are true, $ P \leftrightarrow Q $ is true.
Second Row ($ P = T $, $ Q = F $): Since $ P $ is true and $ Q $ is false, $ P \leftrightarrow Q $ is false.
Third Row ($ P = F $, $ Q = T $): Since $ P $ is false and $ Q $ is true, $ P \leftrightarrow Q $ is false.
Fourth Row ($ P = F $, $ Q = F $): Since both $ P $ and $ Q $ are false, $ P \leftrightarrow Q $ is true.