Question

compound statements directions: use the statements below to write the compound statements. p: vertical angles are congruent q: 15 is a prime number. conjunction ____________ truth value: __________ disjunction __________ truth value: ____________ conditional statements

Explanation:

Step1: Define conjunction

A conjunction $p\land q$ is true only when both $p$ and $q$ are true. Here, $p$: Vertical angles are congruent (which is true), $q$: 15 is a prime number (which is false as $15 = 3\times5$).
$p\land q$: Vertical angles are congruent and 15 is a prime number.

Step2: Determine truth - value of conjunction

Since $q$ is false, the truth - value of $p\land q$ is false.

Step3: Define disjunction

A disjunction $p\lor q$ is false only when both $p$ and $q$ are false.
$p\lor q$: Vertical angles are congruent or 15 is a prime number.

Step4: Determine truth - value of disjunction

Since $p$ is true, the truth - value of $p\lor q$ is true.

Answer:

Conjunction: Vertical angles are congruent and 15 is a prime number; Truth value: false
Disjunction: Vertical angles are congruent or 15 is a prime number; Truth value: true