Question

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 (p and q)
∽p ∨ q (not p or q)
∽p ∧ ∽r (not p and not r)

Answer 1

To write a compound statement for each conjunction or disjunction, replace the variables with the given statements and find the truth value. Example compound statements: '60 seconds = 1 minute and Congruent supplementary angles each have a measure of 90'.

Step-by-step explanation:

To write a compound statement for each conjunction or disjunction, we can replace the variables with the given statements.

p: 60 seconds = 1 minute

q: Congruent supplementary angles each have a measure of 90

r: –12 + 11 < –1

1. p ∧ q (p and q)

Using the statements, this can be written as '60 seconds = 1 minute and Congruent supplementary angles each have a measure of 90'. The truth value of this compound statement depends on whether both p and q are true.

2. ∽p ∨ q (not p or q)

Using the statements, this can be written as '60 seconds does not equal 1 minute or Congruent supplementary angles each have a measure of 90'. The truth value of this compound statement depends on whether at least one of ∽p and q is true.

3. ∽p ∧ ∽r (not p and not r)

Using the statements, this can be written as '60 seconds does not equal 1 minute and –12 + 11 is not less than –1'. The truth value of this compound statement depends on whether both ∽p and ∽r are true.