Logical Arguments

Which of the following can be used to prove that a conditional statement is false?

• counterexample

• converse

• conclusion

• contrapositive

Consider the given statements below:

Ι. If a sphere has a radius of 3 inches, then its surface area is 36π square inches.

ΙΙ. If a sphere has a surface area of 36π square inches, then its volume is 36π cubic inches.

Javier concluded that if a sphere has a radius of 3 inches, then its volume is 36π cubic inches.

Which of the following best describes Javier's conclusion?

• It is false, because statement Ι is false.

• It is false, because statement ΙΙ is false.

• It is false, because Javier used invalid reasoning.

• It is valid by the Law of Detachment

• It is valid by the Law of Syllogism

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the inverse of this statement?

• If the polygon is not a quadrilateral, then it is not a trapezoid.

• If the polygon is not a trapezoid, then it is not a quadrilateral.

• If the polygon is a trapezoid, then it is a quadrilateral.

• A rectangle is also a quadrilateral.

What is it hypothesis in the statement:" If today is Tuesday, then we have school."?

• Tomorrow is Wednesday.

• We have school.

• Today is Tuesday.

• We do not have school.

Which law of logic is this:
If I buy a dress, then I won't get chips.
I bought a dress.
Therefore, I won't get chips.

• Law of Detachment
• Law of Contrapositive
• Law of Syllogism
• Law of Biconditional

Use Law of Syllogism to make a conclusion.
 If a number is divisible by 10, then it is divisible by 2.  If a number is divisible by 2, then it is even.

• If a number is divisible by 10, then it is even,
• If a number is even, then it is divisible by 10.
• If a number is divisible by 2, then it is even.
• If a number is even, then it is divisible by 2.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

If an angle does not have a measure less than 90°, then it is not acute.

• Contrapositive

• Converse

• Biconditional

• Inverse

Which of the following best describes inductive reasoning?

• Drawing a general conclusion from specific observations.

• Using a general principle to predict a specific outcome.

• Formulating a hypothesis based on a single observation.

• Testing a hypothesis through controlled experiments.

Which of the following is an example of inductive reasoning?

• All swans we have seen are white; therefore, all swans are white.

• If it rains, the ground gets wet. It is raining, so the ground is wet.

• Triangles have three sides; therefore, this shape is a triangle.

• If a number is even, then it is divisible by 2.

Which of the following angle pairs are always congruent?

• Corresponding angles

• Alternate interior angles

• Same-side interior angles

• Vertical angles