Logic and Reasoning Answers

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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
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 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.
5

How can the statement be rewritten as a conditional statement in if-then form?The sum of the digits of a two-digit number is less than the value of the original two-digit number.

A
If a number has two digits, then the sum of its digits is less than the value of the original two-digit number.
B
If a number has two digits, then the value of the original two-digit number is less than the sum of its digits.
C
If the sum of the digits of a two-digit number is less than the value of the original two-digit number, then the value of the original two-digit number is greater than the sum of the two digits.
D
If the sum of the digits of a number is less than the value of the original number, then the number is a two-digit number.
6

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
7

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.
9

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.
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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