Law of Detachment and Law of Syllogism

Use the Law of Detachment to draw a conclusion.

Statement 1: If a whole number is even, then its square is divisible by 4.

Statement 2: The number I am thinking of is an even number.

• Then it's not odd.
• Then it's a whole number.
• Then its square is divisible by 4
• Then it's even.

Use the Law of Detachment to draw a conclusion from the two given statements.

Statement 1: If I study for one hour each day, then I will score well on the exam

Statement 2: I will study from 6pm to 7pm tonight.

• I study for several hours each day.

• I will do well on the exam

• If I do well on the exam, I studied for hours.

• not possible

Use the law of syllogism to draw a conclusion from the two given statements:

Statement 1: If you exercise regularly, then you have a healthy body
Statement 2: If you have a healthy body, then you have more energy

• You have more energy
• If you exercise regularly, then you have more energy
• You have a healthy body
• If you do not have a healthy body, then you do not exercise regularly

Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?

Statment 1: If it is snowing heavily, then school will be canceled.
Statement 2: If school is canceled, the big test will not be given today.

• Look out for the snowplows while driving to school.
• It is snowing heavily, then the big test will not be given today.

• It is snowing heavily, then the roads will be hard to drive on.

• It is snowing heavily, then you should call the school to see if school is canceled.

Use Law of Syllogism to make a conclusion.

Statement 1:  If a number is divisible by 10, then it is divisible by 2.  

Statement 2: If a number is divisible by 2, then it is even.

• If a number is divisible by 10, then it is even,
• If a number is even, then it is divisible by 10.
• If a number is divisible by 2, then it is even.
• If a number is even, then it is divisible by 2.

Use the Law of Syllogism to draw a conclusion:

• Statement 1: If I study hard, I will pass the exam.

• Statement 2: If I pass the exam, I will graduate.

• • If I study hard, I will graduate.

• If I study hard, I will pass the class.

• I will graduate and pass the exam.