Logical Conclusions

Front

What is the inverse of the statement: 'If you diet and exercise, then you will lose weight.'?

Back

If you don't diet and exercise, then you will not lose weight.

Front

What is the term for the statement formed by negating both the hypothesis and conclusion of a conditional statement?

Back

Inverse

Front

What is the contrapositive of a conditional statement?

Back

The contrapositive is formed by negating both the hypothesis and conclusion and reversing them.

Front

If a quadrilateral is a square, then it has four congruent sides. What can we conclude if we know that quadrilateral ABCD has four congruent sides?

Back

No valid conclusion possible.

Front

What logical principle allows us to conclude that if 'If I go on a walk, then I will see a dog' and 'If I see a dog, then I will pet the dog', then I will feel happy if I go on a walk?

Back

Law of Syllogism.

Front

If this wind keeps up, then we will lose some trees. We lose some trees. What can we conclude?

Back

No valid conclusion possible.

Front

What is the Law of Detachment?

Back

If 'If P, then Q' is true and P is true, then Q must also be true.

Front

What is a conditional statement?

Back

A statement that can be written in the form 'If P, then Q'.

Front

What is the converse of a conditional statement?

Back

The converse is formed by reversing the hypothesis and conclusion.

Front

If 'If it rains, then the ground is wet' is true, what can we conclude if the ground is wet?

Back

We cannot conclude that it rained; the converse is not necessarily true.