Logic and Reasoning Answers

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Which is a counterexample for the conditional statement?If two positive numbers are multiplied together, then the product will be greater than both of the two positive numbers.

A
2 x 4
B
5 x (−3)
C
Option
Option C
D
Option
Option D
2
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Which conclusion can be drawn based on the true statements shown?If a triangle is equilateral, then all the sides in the triangle are congruent.If all the sides in a triangle are congruent, then all the angles are congruent.

A
Based on the law of syllogism, if all the angles in a triangle are congruent, then the triangle is equilateral.
B
Based on the law of detachment, if all the angles in a triangle are congruent, then the triangle is equilateral.
C
Based on the law of syllogism, if a triangle is equilateral, then all the angles are congruent.
D
Based on the law of detachment, if a triangle is equilateral, then all the angles are congruent.
3

Which is a counterexample for the conditional statement shown?If three distinct points lie in a plane, then the points can form a triangle.

A
The points form a different polygon.
B
The points form a circle.
C
The points form an open figure.
D
The points form a line.
4

Which statement can be concluded using the true statements shown?If two angles in a triangle measure and x degrees, then the third angle measures (90 − x) degrees.In triangle ABC, angle A measures 90 degrees and angle B measures .

Question illustration
A
Angle C must measure 50 degrees.
B
Angle C must measure 40 degrees.
C
Angle C must measure (90 − 40) degrees.
D
Angle C must measure (90 − 30) degrees.
5

If the statement is rewritten as a conditional statement in if-then form, which best describes the conclusion?A student who earns 85% earns a B.

A
If a student earns 85%
B
If a student earns a B
C
Then a student earns 85%
D
Then a student earns a B
6

Galen wrote the statement "If the sum of the digits in a number is divisible by 3, the original number is divisible by 3."Which statements are true regarding his work? Select three options.

A
The hypothesis of the statement is "the sum of the digits in a number is divisible by 3."
B
An equivalent statement is "If the sum of the digits in a number is divisible by 3, then the original number is divisible by 3."
C
The statement is not a conditional statement because it does not include both an "if" and a "then" clause.
D
The statement can be proven true or false.
E
The conclusion of the statement is written before the hypothesis.
7

If the statement shown is rewritten as a conditional statement in if-then form, which best describes the conclusion?When a number is divisible by 9, the number is divisible by 3.

A
Then the number is divisible by 3
B
Then the number is divisible by 9
C
If a number is divisible by 3
D
If a number is divisible by 9
8

How can the statement be rewritten as a conditional statement in if-then form?A rectangle with 4 congruent sides is a square.

A
If a rectangle has 4 congruent sides, then it is a square.
B
If a figure has 4 congruent sides, then it is a square.
C
If a figure has 4 congruent sides, then it is a rectangle or square.
D
If a figure is a rectangle, then it is a square.
9

Which is a counterexample for the conditional statement shown?If two distinct points are graphed on a coordinate plane, then the line connecting the points can be represented with a function.

A
The points have the same x-coordinate value.
B
The points have the same y-coordinate value.
C
The points follow the rule (x, y) (–x, –y).
Option C
D
The points follow the rule (x, y) (–y, –x).
Option D
10

Mr. Thomas wrote these true statements.If a figure is a triangle, the sum of the figure's interior angles is 180.Figure ABC is a triangle.

Question illustration
A
Using the law of detachment, the sum of the interior angles of ABC is 180.
Option A
B
Using the law of detachment, if the sum of a figure’s interior angles is 180, then the figure is a triangle.
Option B
C
Using inductive reasoning, the sum of the interior angles of ABC is 180.
Option C
D
Using inductive reasoning, if the sum of a figure’s interior angles is 180, then the figure is a triangle.
Option D

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