## Problem 1047

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, dis-junction, conditional, or bi-conditional by using both the word and its appropriate symbol.

Statement: If it is raining outside, then we will stay inside.

Solution:-

Sentences that convey only one idea are called simple statement. Statements consisting of two or more simple statements are called compound statements.

A negation change a statement to its opposite meaning. A conjunction is an ‘and’ statement, and a dis-junction is an ‘or’ statement. A conditional is an ‘if-than’ statement, and a bi-conditional is an ‘if and only if’ statement.

There are two simple statement contained in the statement above: “it is raining outside,” “and “we will stay inside.”

Since there are two simple statement contained in the statement, it is a compound statement.

The “If….then” words in the statement indicate that it is a conditional compound statement.

## Identify conditional equations, contradictions, and identities

Identify conditional equations, contradictions, and identities

All of the preceding equations had solution sets containing one element; for example, 2(k – 5) + 3k =  k + 6 has solution set {4}. Some linear equations, however, have no solutions, while others have an infinite number of solutions. The table on the next page gives the names of these types of equations.