Question

Question worth 10 points

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.

r ∧ (q ∨ s)

Select one:
A. Four points are always coplanar, or a right angle measures 90° and a decagon has 12 sides; false.

B. Four points are always coplanar, and a right angle measures 90° or a decagon has 12 sides; true.

C. Four points are always coplanar, or a right angle measures 90° and a decagon has 12 sides; true.

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

Answer 1

Options b and D

Explanation:

It's a question of Boolean's algebra

We will find the truth values of each statement p, q, r, and s first.

p : An isosceles triangle has two congruent sides.

Means truth value is True

q ; A right angle measures 90°

Truth value of this statement will be True

r : Four Points are always coplanar.

Truth value of this statement will be False.

s : A decagon has 12 sides

Truth value of the statement will be False.

Now we come to the options.

a. Four points are always coplanar and a right angle measures 90°.

Here "and" means conjunction and truth value of conjuncion of two statements will be true if only both the statements are true.

r q r ∧ q

T T T

But the truth value is given as false so not the correct option.

b. Four points are always coplanar and a right angle measures 90°.

As we have discussed in option a. truth value of the conjunction is True so this option will be the correct option.

c. Four points are always coplanar or a right angle measures 90°

OR means it's a disjunction and truth value of disjunction is false only when both the statements are False.

r q r ∨ q

T T T

But the truth value is given as False, so this option is not correct.

d. Four points are always coplanar or a right angle measure 90°

As discussed in option c. Truth value will be True. so this option will be the correct option.

Options b and d are the correct options.