The truth table for ~p ↔ ~q shows that the biconditional is true when the negations of p and q have the same truth value, and false otherwise. It helps analyze logical relationships in different scenarios.
Here's how the truth values are derived:
~p is the negation of p.
~q is the negation of q.
~p ↔ ~q is the biconditional (if and only if) between ~p and ~q
The truth table for the statement ~p ↔ ~q involves evaluating the logical connective biconditional, denoted as ↔, between the negation of p (~p) and the negation of q (~q). In each row, the truth values of p and q are considered, and their negations are determined.
The biconditional operation then checks whether ~p and ~q have the same truth value. When both ~p and ~q are either true or false, ~p ↔ ~q evaluates to true; otherwise, it is false.
The resulting truth table provides a systematic representation of the logical relationships between the given statements, helping to analyze the conditions under which the biconditional statement holds true or false.