Question

Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value

p. An isosceles triangle has two congruent sides
q: A right angle
r Four points
s: A decagon has 12 sides.

A right measures 90° measures 90° and an isosceles triangle has two congruent sides; true
A right angle measures 90° or an isosceles triangle has two congruent sides; true oytb
A right angle A right angle measures 90° and an isosceles triangle does not have two congruent sides; false
A right angle measures 90° or an isosceles triangle does not have two congruent sides; true.

Answer 1

A compound statement is formed as either a conjunction or disjunction using the given facts; both the statement that a right angle measures 90° and an isosceles triangle has two congruent sides (conjunction) and the statement that a right angle measures 90° or an isosceles triangle has two congruent sides (disjunction) are true.

Step-by-step explanation:

The question asks us to form a compound statement using the provided statements and then determine its truth value. A conjunction is a compound statement that is true if both of its components are true; a disjunction is a compound statement that is true if at least one of its components is true. In this case, we can create two compound statements:

• A right angle measures 90° and an isosceles triangle has two congruent sides.
• A right angle measures 90° or an isosceles triangle has two congruent sides.

For the conjunction, since both statements are true, the compound statement is true. For the disjunction, since at least one of the statements is true, the compound statement is also true. In logic and mathematics, understanding the validity of compound statements and their truth values is essential, as they can be used to construct logical arguments and prove mathematical theorems.