Laws of Logic

Front

What is the Law of Detachment?

Back

The Law of Detachment states that if a conditional statement is true and the hypothesis is true, then the conclusion must also be true.

Front

What is the Law of Syllogism?

Back

The Law of Syllogism states that if 'p implies q' and 'q implies r' are both true, then 'p implies r' is also true.

Front

What is the Law of Contrapositive?

Back

The Law of Contrapositive states that a conditional statement 'if p then q' is logically equivalent to 'if not q then not p'.

Front

What is a conditional statement?

Back

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

Front

What does 'p → q' mean in logic?

Back

'p → q' means 'if p is true, then q is also true'.

Front

What is the contrapositive of 'If it rains, then the ground is wet'?

Back

The contrapositive is 'If the ground is not wet, then it does not rain'.

Front

What is the difference between a hypothesis and a conclusion in a conditional statement?

Back

The hypothesis is the 'if' part, and the conclusion is the 'then' part of a conditional statement.

Front

Provide an example of the Law of Detachment.

Back

If it is snowing (p), then school is canceled (q). It is snowing. Therefore, school is canceled.

Front

What is the symbolic representation of 'If I do not study, then I will not pass'?

Back

~p → ~q, where p is 'I study' and q is 'I pass'.

Front

What is an example of the Law of Syllogism?

Back

If it is a holiday (p), then the store is closed (q). If the store is closed (q), then I cannot buy groceries (r). Therefore, if it is a holiday (p), then I cannot buy groceries (r).