laws of detachment and syllogism

What is the Inverse of a Conditional Statement?

• If p, then q

• If not p, then not q

• If q, then p

• If not q, then not p

What is a Conditional Statement?

• A statement that expresses a relationship between two propositions.

• A statement that can be either true or false.

• A statement that provides a command or request.

• A statement that describes a fact or opinion.

What is the Converse of a Conditional Statement?

• If p, then q

• If q, then p

• If p, then not q

• If not p, then q

What is the Contrapositive of a Conditional Statement?

• If p, then q

• If not p, then not q

• If not q, then not p

• If q, then p

Define Deductive Reasoning.

• Deductive Reasoning is the process of reasoning logically from given statements or facts to a conclusion.

• Deductive Reasoning is a method of making decisions based on personal opinions and beliefs.

• Deductive Reasoning involves guessing the outcome based on previous experiences.

• Deductive Reasoning is the process of collecting data to support a hypothesis.

What is a valid conclusion?

• A conclusion that is based on personal opinion.

• A conclusion that logically follows from the premises or statements provided.

• A conclusion that is always true regardless of the premises.

• A conclusion that is drawn from emotional reasoning.

What is the difference between Deductive and Inductive Reasoning?

• Deductive Reasoning starts with specific observations and formulates general conclusions, while Inductive Reasoning starts with general statements and reaches a specific conclusion.

• Deductive Reasoning starts with general statements and reaches a specific conclusion, while Inductive Reasoning starts with specific observations and formulates general conclusions.

• Both Deductive and Inductive Reasoning start with general statements and reach specific conclusions.

• Deductive Reasoning and Inductive Reasoning are the same and can be used interchangeably.

What is an example of the Law of Syllogism?

• If it is snowing, then school is canceled. If school is canceled, then the big test is not given. Therefore, if it is snowing, then the big test is not given.

• If it is raining, then the ground is wet. If the ground is wet, then the flowers grow. Therefore, if it is raining, then the flowers grow.

• If it is sunny, then the park is crowded. If the park is crowded, then there are no available benches. Therefore, if it is sunny, then there are no available benches.

• If it is foggy, then visibility is low. If visibility is low, then driving is dangerous. Therefore, if it is foggy, then driving is dangerous.

What does it mean for a statement to be true?

• A statement is true if it accurately reflects reality or is consistent with the facts.

• A statement is true if it is popular among people.

• A statement is true if it sounds good when spoken aloud.

• A statement is true if it is written in a book.

How do you form a conclusion using the Law of Syllogism?

• Identify two true conditional statements where the conclusion of one statement matches the hypothesis of the other.

• Use any two statements regardless of their truth value.

• Formulate a conclusion based on personal opinion rather than logical reasoning.

• Combine unrelated statements to create a new conclusion.