Embark on an intellectual journey with our comprehensive “Law of Detachment and Law of Syllogism Worksheet with Answers.” This guide delves into the intricacies of logical reasoning, empowering you with the tools to navigate arguments with precision and clarity.

Prepare to unravel the complexities of deductive arguments as we explore the fundamental principles of the Law of Detachment and the Law of Syllogism. Engage in thought-provoking exercises designed to sharpen your critical thinking skills and solidify your understanding of these essential logical concepts.

Law of Detachment and Law of Syllogism

In propositional logic, the law of detachment and the law of syllogism are two rules of inference that allow us to derive new propositions from given propositions.

Law of Detachment

The law of detachment states that if we have a conditional proposition (if P then Q) and we know that the antecedent (P) is true, then we can conclude that the consequent (Q) is also true.

• P → Q
• P
• Therefore, Q

For example, if we know that “if it is raining, then the ground is wet” and we observe that it is raining, then we can conclude that the ground is wet.

The law of detachment is closely related to the rule of modus ponens, which allows us to derive a new proposition by combining a conditional proposition and a proposition that affirms the antecedent.

Law of Syllogism

The law of syllogism states that if we have two conditional propositions (if P then Q and if Q then R) and we know that the antecedent of the first proposition (P) is true, then we can conclude that the consequent of the second proposition (R) is also true.

• P → Q
• Q → R
• P
• Therefore, R

For example, if we know that “if it is raining, then the ground is wet” and “if the ground is wet, then the grass is wet” and we observe that it is raining, then we can conclude that the grass is wet.

The law of syllogism is a powerful tool for deductive reasoning, as it allows us to derive new conclusions from a set of given propositions.

Worksheet with Answers, Law of detachment and law of syllogism worksheet with answers

Instructions:

1. Use the law of detachment to derive the conclusion from the given premises.
2. Use the law of syllogism to derive the conclusion from the given premises.

Problems:Law of Detachment

• If it is raining, then the ground is wet. It is raining.
• If you study hard, you will pass the exam. You did not study hard.

Law of Syllogism

• If it is raining, then the ground is wet. If the ground is wet, then the grass is wet. It is raining.
• If you are a student, then you are enrolled in a school. If you are enrolled in a school, then you have a student ID. You are a student.

Answers:Law of Detachment

• The ground is wet.
• You will not pass the exam.

Law of Syllogism

• The grass is wet.
• You have a student ID.
  

  FAQ Corner: Law Of Detachment And Law Of Syllogism Worksheet With Answers

  What is the Law of Detachment?

The Law of Detachment states that if a conditional statement is true and its antecedent is true, then its consequent must also be true.

How do I apply the Law of Syllogism?

To apply the Law of Syllogism, you need three statements: a major premise, a minor premise, and a conclusion. The major premise states a general rule, the minor premise applies the rule to a specific case, and the conclusion follows logically from the two premises.