Ch.2 Deductive Reasoning Postulate

What is a conditional statement?

• A conditional statement is a programming construct that allows the execution of different code blocks based on a specified condition.

• A conditional statement is a function that returns a random number between two specified values.

• A conditional statement is a loop that repeats a block of code until a specified condition is met.

• A conditional statement is a data type that stores a true or false value.

State the Law of Detachment.

• If p -> q is a true statement and p is false, then q is also true.

• If p -> q is a true statement and p is true, then q is also true.

• If p -> q is a false statement and p is true, then q is also true.

• If p -> q is a true statement and p is true, then q is also false.

What is the Law of Syllogism?

• A logical rule that states if the first statement implies the second statement, and the second statement implies the fourth statement, then the first statement implies the second statement.

• A logical rule that states if the first statement implies the second statement, and the second statement implies the first statement, then the first statement implies the first statement.

• A logical rule that states if the first statement implies the second statement, and the second statement implies the fourth statement, then the first statement implies the fourth statement.

• A logical rule that states if the first statement implies the second statement, and the second statement implies the third statement, then the first statement implies the third statement.

Define contrapositive.

• The contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion of the original statement and then switching their positions.

• The contrapositive of a conditional statement is formed by switching the positions of the hypothesis and the conclusion without negating them.

• The contrapositive of a conditional statement is formed by negating the conclusion of the original statement.

• The contrapositive of a conditional statement is formed by negating the hypothesis of the original statement.

Explain the concept of inverse.

• Inverse is a mathematical operation that has no effect on another operation.

• Inverse is a term used in computer programming to describe a loop that repeats indefinitely.

• Inverse is a concept used only in geometry.

• Inverse is a mathematical operation that reverses the effect of another operation.

What is the purpose of conditional statements in deductive reasoning?

• The purpose of conditional statements in deductive reasoning is to establish logical relationships between statements or propositions.

• To introduce irrelevant information

• To make the reasoning more complicated

• To confuse the reader

How is the Law of Detachment used in logical reasoning?

• The Law of Detachment is used to analyze the structure of logical arguments.

• The Law of Detachment is used to prove the validity of mathematical equations.

• The Law of Detachment is used to draw valid conclusions from conditional statements.

• The Law of Detachment is used to determine the truth value of statements.

Give an example of the Law of Syllogism.

• If all humans are immortal (p implies q) and Socrates is a human (q implies r), then Socrates is immortal (p implies r).

• If all humans are mortal (p implies q) and Socrates is not a human (q implies r), then Socrates is mortal (p implies r).

• If all humans are mortal (p implies q) and Socrates is a dog (q implies r), then Socrates is mortal (p implies r).

• If all humans are mortal (p implies q) and Socrates is a human (q implies r), then Socrates is mortal (p implies r).

Why is contrapositive important in deductive reasoning?

• To make the argument more complex

• To confuse the audience

• To provide alternative explanations

• To prove the validity of an argument

Provide an example of an inverse statement.

• If it is raining, then the ground is wet.

• If the ground is wet, then it is raining.

• If it is not raining, then the ground is wet.

• If it is not raining, then the ground is not wet.