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Beginning Activity Beginning Activity 2: Truth Values of Statements
A4US

We will use the following two statements for all of this activity:

\(P\) is the statement “It is raining.”
\(Q\) is the statement “Daisy is playing golf.”

In each of the following four parts, a truth value will be assigned to statements \(P\) and \(Q\text{.}\) For example, in Question (1), we will assume that each statement is true. In Question (2), we will assume that \(P\) is true and \(Q\) is false. In each part, determine the truth value of each of the following statements:

List 2.1. Statements

  1. \(\left( P \wedge Q \right)\) It is raining and Daisy is playing golf.

  2. \(\left( P \vee Q \right)\) It is raining or Daisy is playing golf.

  3. \(\left( P \to Q \right)\) If it is raining, then Daisy is playing golf.

  4. \(\left( \mynot P \right)\) It is not raining.

Which of the four statements in List 2.1 are true and which are false in each of the following four situations?

1.

When \(P\) is true (it is raining) and \(Q\) is true (Daisy is playing golf).

2.

When \(P\) is true (it is raining) and \(Q\) is false (Daisy is not playing golf).

3.

When \(P\) is false (it is not raining) and \(Q\) is true (Daisy is playing golf).

4.

When \(P\) is false (it is not raining) and \(Q\) is false (Daisy is not playing golf).