Logical Conclusions

Can a valid conclusion be made?

If I go to the movie, then I’ll eat popcorn.

If I eat popcorn, then I’ll enjoy the movie.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

• Yes, using the Law of Contrapositives

Can a valid conclusion be made?

If a figure is a square, then it is a rectangle.

If a figure is a rectangle, then it has 4 right angles.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

• Yes, using the Law of Contrapositives

Can a valid conclusion be made?

If I miss my bus, then I’ll be late for school.

I missed my bus.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

• Yes, using the Law of Contrapositives

Can a valid conclusion be made?

If this wind keeps up, then we will lose some trees.

We lost some trees.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

• Yes, using the Law of Contrapositives

Can a valid conclusion be made?

All accountants enjoy mathematics.

People who enjoy mathematics are intelligent.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

• Yes, using the Law of Contrapositives

Can a valid conclusion be made?

If a person is a librarian, then they read books.

If a person is a friend of Dana’s, then they read books.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

• Yes, using the Law of Contrapositives

Can a valid conclusion be made?

If an animal is a pig, then it is a mammal.

Leon is a pig.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

• Yes, using the Law of Contrapositives

Can a valid conclusion be made?

If a quadrilateral is a square, then it has four congruent sides.

Quadrilateral ABCD has four congruent sides.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

• Yes, using the Law of Contrapositives

Can a valid conclusion be made?

If my mother lets me go to a movie, then I will be happy.

My mom lets me go to a movie.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

• Yes, using the Law of Contrapositives

Can a valid conclusion be made?

If a man is wealthy, then he buys a mansion.

If a man can buy a mansion, then he can hire a housekeeper.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

• Yes, using the Law of Contrapositives