HW 2.3

Front

What is the Law of Syllogism?

Back

The Law of Syllogism states that if 'p implies q' and 'q implies r', then 'p implies r'. It allows for drawing a conclusion from two conditional statements.

Front

What is the Law of Detachment?

Back

The Law of Detachment states that if 'p implies q' is true and 'p' is true, then 'q' must also be true.

Front

What is the Law of Contrapositive?

Back

The Law of Contrapositive states that if 'p implies q' is true, then 'not q implies not p' is also true.

Front

What is a valid conclusion?

Back

A valid conclusion is a logical deduction that follows from given premises or statements.

Front

If it is snowing heavily, then school will be canceled. If school is canceled, the big test will not be given today. What is the conclusion?

Back

The big test will not be given today.

Front

If Jack goes to school, then it is Monday. Jack doesn't go to school. What can we conclude?

Back

Invalid conclusion; we cannot determine if it is Monday.

Front

What does 'p → q' represent in logic?

Back

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

Front

What is an example of the Law of Syllogism?

Back

If 'p: It is raining' implies 'q: The ground is wet', and 'q: The ground is wet' implies 'r: The flowers are blooming', then 'p: It is raining' implies 'r: The flowers are blooming'.

Front

What is the difference between a valid and an invalid argument?

Back

A valid argument has a conclusion that logically follows from its premises, while an invalid argument does not.

Front

What is a conditional statement?

Back

A conditional statement is an 'if-then' statement that expresses a relationship between two propositions.