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 measures 90°.
r: Four points are always coplanar.
s: A decagon has 12 sides.

(q∧r) ∨s

a. A right angle measures 90° or four points are always coplanar, and a decagon has 12 sides; false.
b. A right angle measures 90° and four points are always coplanar, or a decagon has 12 sides; false.
c. A right angle measures 90° and four points are always coplanar, or a decagon has 12 sides; true.
d. A right angle measures 90° or four points are always coplanar, and a decagon has 12 sides; true.

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sqdancefan sqdancefan · Answer 1 · 2019-07-28T00:15:03+02:00

Answer:

b. A right angle measures 90° and four points are always coplanar, or a decagon has 12 sides; false.

Step-by-step explanation:

∧ = "and"

∨ = "or"

So, the symbols translate to

(q∧r)∨s = (A right angle measures 90° ∧ Four points are always coplanar) ∨ A decagon has 12 sides

This matches the wording of choices B and C.

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The truth values are ...

so the expression evaluates to

(true ∧ false) ∨ false = false ∨ false = false . . . matches choice B