Question

question 15 (1 point) use the following statements to write a compound statement for each conjunction or disjunction. then find its truth - value. p: 60 seconds = 1 minute q: congruent supplementary angles each have a measure of 90. r: - 12+11 < - 1 p∧q a) 60 seconds = 1 minute and congruent supplementary angles each have a measure of 90; false. b) 60 seconds = 1 minute or congruent supplementary angles each have a measure of 90; false. c) 60 seconds = 1 minute or - 12+11≥ - 1; true. d) 60 seconds = 1 minute or - 12+11 < - 1; false.

Explanation:

Step1: Recall logical connectives

A conjunction ($p\land q$) is true only when both $p$ and $q$ are true. A disjunction ($p\lor q$) is true when at least one of $p$ or $q$ is true.

Step2: Evaluate individual statements

• For $p$: 60 seconds = 1 minute is a true statement.
• For $q$: Congruent supplementary angles each have a measure of 90 is a true statement (since if two angles are supplementary their sum is 180, and if they are congruent then each is 90).
• For $r$: - 12+11 < - 1, calculate - 12 + 11=-1, and - 1 is not less than - 1, so $r$ is false.

Step3: Analyze the compound statements

We want to find the truth - value of $
eg p\land q$. Since $p$ is true, $
eg p$ is false. And $q$ is true. A conjunction $
eg p\land q$ is false when one of the statements is false. So $
eg p\land q$ is false.

Answer:

False