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Chapter 3: Problem 18

Construct a truth table for the given statement. \(\sim p \leftrightarrow q\)

Short Answer

Expert verified
The truth table for the described logic statement is as follows: - If p and q are both true, then \(\sim p \leftrightarrow q\) is false. - If p is true and q is false, then \(\sim p \leftrightarrow q\) is true. - If p is false and q is true, then \(\sim p \leftrightarrow q\) is true. - If p and q are both false, then \(\sim p \leftrightarrow q\) is false.

Step by step solution

01

Defining the Propositions

Define the two propositions p and q. In the truth table, there are four possible combinations of truth values for p and q - both can be either true or false.
02

Calculate the Negation of p

Now, calculate the negation of proposition p, denoted by \(\sim p\). If p is true, \(\sim p\) is false, and if p is false, \(\sim p\) is true.
03

Compare the Values

Lastly, for each possible combination of p and q, the given statement is true if \(\sim p\) has the same truth value as q. Otherwise, it's false. Write these values down in the table as a result for the statement \(\sim p \leftrightarrow q\).

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