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Beginning Activity Beginning Activity 2: Conditional Statements
A4US

Given statements P and Q, a statement of the form “If P then Q” is called a conditional statement. It seems reasonable that the truth value (true or false) of the conditional statement “If P then Q” depends on the truth values of P and Q. The statement “If P then Q” means that Q must be true whenever P is true. The statement P is called the hypothesis of the conditional statement, and the statement Q is called the conclusion of the conditional statement. We will now explore some examples.

1.

“If it is raining, then Laura is at the theater.” Under what conditions is this conditional statement false? For example,

(a)

Is it false if it is raining and Laura is at the theater?

(b)

Is it false if it is raining and Laura is not at the theater?

(c)

Is it false if it is not raining and Laura is at the theater?

(d)

Is it false if it is not raining and Laura is not at the theater?

2.

Identify the hypothesis and the conclusion for each of the following conditional statements.

(a)

If x is a positive real number, then x is a positive real number.

(b)

If x is not a real number, then x is a negative real number.

(c)

If the lengths of the diagonals of a parallelogram are equal, then the parallelogram is a rectangle.