EDGE Math 8

Types of Statements

You can combine two or more statements using logical connectives like and, or, if…then, and if and only if.

CONJUNCTIONS OF STATEMENTS

Definition

A conjunction consists of two or more statements connected by the word "and."

The conjunction of statements p and q results in "p and q." The following table shows the possible truth values of statements p and q, as well as the corresponding truth values of their conjunctions:

Truth Table of Conjunctions of Statements

p	q	p and q
true	true	true
true	false	false
false	true	false
false	false	false

Example

Determine the truth value of each conjunction.

1.	8 is even and 7 is odd.
2.	Angle B, which measures 53°, is an acute angle and $∠ C,$ which measures 89°, is an obtuse angle.

Solution

1.	The statement "8 is even" is true and the statement "7 is odd" is also true. Thus, the truth value of their conjunction is true.

2.	The statement "Angle B, which measures 53°, is an acute angle" is true, and the statement " $∠ C,$ which measures 89°, is an obtuse angle," is false. Thus, the truth value of their conjunction is false.

Note that the conjunction of a statement p and its negation, not p, is always false. Such a statement is called a contradiction.