Deductive Reasoning

Front

What is Deductive Reasoning?

Back

Deductive reasoning is a logical process where a conclusion is reached by applying general principles to specific cases. It involves starting with a general statement or hypothesis and examining the possibilities to reach a specific, logical conclusion.

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

Front

What is the Law of Detachment?

Back

The Law of Detachment states that if a conditional statement (p → q) is true and the antecedent (p) is true, then the consequent (q) must also be true.

Front

What is the Law of Syllogism?

Back

The Law of Syllogism states that if the first statement (p → q) and the second statement (q → r) are both true, then the conclusion (p → r) is also true.

Front

What is the Law of Contrapositive?

Back

The Law of Contrapositive states that if a conditional statement (p → q) is true, then its contrapositive (¬q → ¬p) is also true.

Front

Provide an example of the Law of Detachment.

Back

If it rains, then the ground is wet. It is raining. Therefore, the ground is wet.

Front

Provide an example of the Law of Syllogism.

Back

If it is a holiday, then the store is closed. If the store is closed, then I cannot buy groceries. Therefore, if it is a holiday, then I cannot buy groceries.

Front

What is a conditional statement?

Back

A conditional statement is a logical statement that has two parts: a hypothesis (p) and a conclusion (q), typically written in the form 'If p, then q'.

Front

What does 'p → q' represent?

Back

The expression 'p → q' represents a conditional statement where p is the hypothesis and q is the conclusion.

Front

What is the contrapositive of the statement 'If it is sunny, then we will go to the beach'?

Back

The contrapositive is 'If we do not go to the beach, then it is not sunny'.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Front

How can you use the Law of Syllogism in reasoning?

Back

You can use the Law of Syllogism to connect two conditional statements to draw a new conclusion based on the relationships between the statements.