Question

question 3 (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 q ∨ r a. congruent supplementary angles each have a measure of 90 or - 12 + 11 < - 1; false. b. congruent supplementary angles each have a measure of 90 and - 12 + 11 < - 1; false. c. congruent supplementary angles each have a measure of 90 and - 12 + 11 < - 1; true. d. congruent supplementary angles each have a measure of 90 or - 12 + 11 < - 1; true. question 4 (1 point) complete each truth - table.

Explanation:

Step1: Analyze statement p

Statement p: 60 seconds = 1 minute is a well - known and always true fact.

Step2: Analyze statement q

Statement q: Congruent supplementary angles each have a measure of 90. Supplementary angles add up to 180 degrees. If they are congruent, each is 90 degrees, so this is true.

Step3: Analyze statement r

Solve the inequality \(r:-12 + 11<-1\). Calculate \(-12 + 11=-1\), and \(-1
ot<-1\), so the statement \(-12 + 11<-1\) is false.

Step4: Analyze conjunctions and disjunctions

For \(p\land q\) (conjunction of p and q)

Since both p and q are true, by the definition of a conjunction (true only when both parts are true), \(p\land q\) is true.

For \(p\lor r\) (disjunction of p and r)

Since p is true, and a disjunction is true when at least one of the statements is true, \(p\lor r\) is true.

For \(q\land r\) (conjunction of q and r)

Since r is false, \(q\land r\) is false.

For \(q\lor r\) (disjunction of q and r)

Since q is true, \(q\lor r\) is true.

Answer:

For \(p\land q\): True
For \(p\lor r\): True
For \(q\land r\): False
For \(q\lor r\): True