Beginning Activity 2: Truth Values of Statements

Beginning Activity Beginning Activity 2: Truth Values of Statements
A4 US

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 $Q .$ 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

$(P \land Q)$ It is raining and Daisy is playing golf.
$(P \lor Q)$ It is raining or Daisy is playing golf.
$(P \to Q)$ If it is raining, then Daisy is playing golf.
$(\neg P)$ 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).

Mathematical Reasoning: Writing and Proof (PreTeXt Edition)

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