# Construct a truth table for the given statement. [ p ↔ ( q → ∼ r ) ] ∧ ∼ q

### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

Chapter
Section

### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 3, Problem 33RE
Textbook Problem
1 views

## Construct a truth table for the given statement. [ p ↔ ( q → ∼ r ) ] ∧ ∼ q

To determine

To construct::

A truth value of the given statement.

### Explanation of Solution

Given information::

The given statement [p(q~r)]~q

Concept Involved:

 The negation of statement p is "not p." The negation of p is symbolized by "~p." The truth value of ~p is the opposite of the truth value of p. A disjunction is a compound statement formed by joining two statements with the connector OR. The disjunction "p or q" is symbolized by p∨  q. A disjunction is false if and only if both statements are false; otherwise it is true. A conjunction is a compound statement formed by joining two statements with the connector AND. The conjunction "p and q" is symbolized by   p∧q. A conjunction is true when both of its combined parts are true; otherwise it is false. A conditional statement, symbolized by  p→q, is an if-then statement in which p is a hypothesis and q is a conclusion. The conditional is defined to be true unless a true hypothesis leads to a false conclusion. A biconditional statement is defined to be true whenever both parts have the same truth value. The biconditional p↔q represents "p if an only if q", where p is a hypothesis and q is a conclusion.

Calculation:

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