Deductive Reasoning - Laws of Detachment & Syllogism

True or False?

Given: If I brush my teeth, then I won't get cavities.

Given: I brush my teeth.

Conclusion: I won't get cavities.

• True; Law of Detachment

• True; Law of Syllogism

• False; Invalid

True or False?

Given: If it rains, then I will use my umbrella.

Given: If it rains, then I will wear my rain boots.

Conclusion: If I use my umbrella, then I will wear my rain boots.

• True; Law of Detachment

• True; Law of Syllogism

• False; Invalid

True or False?

Given: If Amy goes to a Mexican restaurant, then she will order queso.

Given: If she orders queso, then she will eat two baskets of chips.

Conclusion: If Amy goes to a Mexican restaurant, then she will eat two baskets of chips.

• True; Law of Detachment

• True; Law of Syllogism

• False; Invalid

True or False?

Given: If Deion watches football, then he will cheer for the home team.

Given: Deion watches football.

Conclusion: Deion cheers for the home team.

• True; Law of Detachment

• True; Law of Syllogism

• False; Invalid

True or False?

Given: If I read a book, then I gain more knowledge.

Given: If I gain more knowledge, then I share it with my friends.

Conclusion: If I read a book, then I share knowledge with my friends.

• True; Law of Detachment

• True; Law of Syllogism

• False; Invalid

True or False?

Given: If I go to my grandma's house, then I will eat chocolate chip cookies.

Given: I ate chocolate chip cookies.

Conclusion: I went to my grandma's house.

• True; Law of Detachment

• True; Law of Syllogism

• False; Invalid

True or False?
Given: If we win all our soccer games, then we will get a trophy.

Given: We win all our soccer games.

Conclusion: We will get a trophy.

• True; Law of Detachment

• True; Law of Syllogism

• False; Invalid

True or False?

Given: If Jake has Allstate insurance, then he will avoid mayhem.

Given: If Jake avoids mayhem, then his insurance is discounted.

Conclusion: If Jake's insurance is discounted, then he has Allstate insurance.

• True; Law of Detachment

• True; Law of Syllogism

• False; Invalid

True or False?

Given: If a whole number is divisible by 12, then it is divisible by 6.

Given: If a whole number is divisible by 6, then it is divisible by 2 and 3.

Conclusion: If a whole number is divisible by 12, then it is divisible by 2 and 3.

• True; Law of Detachment

• True; Law of Syllogism

• False; Invalid

True or False?

Given: If each angle in a triangle is less than 90°, then it is an acute triangle.

Given: Each angle in a triangle is less than 90°.

Conclusion: The triangle is an acute triangle.

• True; Law of Detachment

• True; Law of Syllogism

• False; Invalid