MATH SOLVE

4 months ago

Q:
# Question worth 10 pointsUse 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.

Accepted Solution

A:

Answer:Options b and DStep-by-step explanation:It's a question of Boolean's algebraWe 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 Trueq ; A right angle measures 90°Truth value of this statement will be Truer : Four Points are always coplanar.Truth value of this statement will be False.s : A decagon has 12 sidesTruth 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 ∧ qT T TBut 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 ∨ qT T TBut 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.