2.4 Truth Tables for the Conditional and Biconditional

Why an if-then fails only when a true premise yields a false conclusion, when a two-way implication holds, and how to test validity by table.

Contemporary Mathematics, 2.4 Truth Tables for the Conditional and Biconditional

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4 exercises

2.4 Exercise 1

Assume both of the following statements are true: $p$ : My sibling washed the dishes, and $q$ : My parents paid them $5.00. Create a truth table to determine the truth value of each of the following conditional statements.

$p \rightarrow q$
$p \rightarrow \text{ } \sim q$
$\sim p \rightarrow q$

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2.4 Exercise 3

Construct a truth table to analyze all possible outcomes for each of the following statements then determine whether they are valid.

$p \land q \rightarrow \sim q$
$p \rightarrow \sim p \lor q$

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2.4 Exercise 5

Assume both of the following statements are true: $p$ : The plumber fixed the leak, and $q$ : The homeowner paid the plumber $150.00. Create a truth table to determine the truth value of each of the following biconditional statements.

$p \leftrightarrow q$
$p \leftrightarrow \text{ } \sim q$
$\sim p \leftrightarrow \text{ } \sim q$

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2.4 Exercise 7

Construct a truth table to analyze all possible outcomes for each of the following statements, then determine whether they are valid.

$p \land q \leftrightarrow p \land \sim q$
$p \lor q \leftrightarrow \sim p \lor q$
$p \rightarrow q \leftrightarrow \sim q \rightarrow \sim p$
$p \land q \rightarrow \sim r \leftrightarrow p \land q \land r$

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