Laws of Logic

Front

What is the Law of Detachment in logic?

Back

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

Front

Provide an example of the Law of Detachment.

Back

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

Front

What is the Law of Syllogism in logic?

Back

The Law of Syllogism states that if 'p implies q' and 'q implies r', then 'p implies r'.

Front

Provide an example of the Law of Syllogism.

Back

If it is a dog, then it is an animal. If it is an animal, then it has a heartbeat. Therefore, if it is a dog, then it has a heartbeat.

Front

What is a conditional statement?

Back

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

Front

What does it mean if a conditional statement is true?

Back

A conditional statement is true unless the hypothesis is true and the conclusion is false.

Front

What is the contrapositive of a conditional statement?

Back

The contrapositive of a conditional statement 'If p, then q' is 'If not q, then not p'. It is logically equivalent to the original statement.

Front

What is the difference between a valid argument and a sound argument?

Back

A valid argument is one where if the premises are true, the conclusion must be true. A sound argument is a valid argument with true premises.

Front

What is a biconditional statement?

Back

A biconditional statement is a statement that combines two conditional statements, stating that both conditions are true or both are false, often written as 'p if and only if q'.

Front

What is a fallacy in logic?

Back

A fallacy is an error in reasoning that renders an argument invalid.