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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
2
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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
3

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.
4

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.
5

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
6

Inductive reasoning is based on

A
definitions.
B
facts.
C
patterns.
D
rules.
7

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.
8

Which is a counterexample for the conditional statement?If a square has side length s, then the perimeter is less than the area.

A
s = 3
B
s = 5
C
s = 7
D
s = 9
9

Branden and Janna are analyzing the same conditional statement. Branden finds multiple examples that validate the conditional statement. Janna finds one example that satisfies the hypothesis of the conditional statement, but not the conclusion. Which must be true?

A
The conditional statement is true. There are more examples that validate the statement than there are that do not.
B
The conditional statement is true. There is at least one example that validates the statement.
C
The conditional statement is false. There is at least one counterexample for the statement.
D
The conditional statement is false. There must be exactly one example that validates the statement.
10

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.

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