3-3: Deductive Reasoning

3-3: Deductive Reasoning

Today's Goals

• Apply the Law of Detachment to determine the validity of conclusions.

• Apply the Law of Syllogism to make valid conclusions from statements.

Multiple Choice

Determine whether the conclusion is based on inductive or deductive reasoning.

• Inductive Reasoning

• Deductive Reasoning

Multiple Choice

Determine whether the conclusion is based on inductive or deductive reasoning.

• Inductive Reasoning

• Deductive Reasoning

Multiple Choice

Determine whether the conclusion is valid based on the given information. Select the correct answer and justification.

• Valid; points A, B, and C determine plane G. Therefore, they are noncollinear.

• Valid; because points A, B, and C are noncollinear, they determine plane G.

• Invalid; points A, B, and C determine plane G. Therefore, they are noncollinear.

• Invalid; points A, B, and C can be collinear and lie in plane G.

Multiple Choice

Determine whether the conclusion is valid based on the given information. Select the correct answer and justification.

• Invalid; because the statement Dakota bought a new game does not satisfy the hypothesis of the conditional statement, the conclusion is not true.

• Valid; because the statement Dakota went to the video game store this afternoon satisfies the conclusion of the conditional statement, the hypothesis of the conditional is true.

• Valid; because the statement Dakota went to the video game store this afternoon satisfies the hypothesis of the conditional statement, the conclusion is true.

• Invalid; because the statement Dakota went to the video game store this afternoon satisfies only the hypothesis, the conclusion is not true.