Logic Review

Let p represent: Brent works this summer.

Let q represent: Brent takes a vacation.

What is the symbolic representation of this statement?

Therefore, Brent does not work this summer.

• ∴~p

• ∴~q

• ~p

• ~q

Given, "If angles are congruent, then the measures of the angles are equal." Identify the contrapositive.

• If the measures of the angles are equal, then the angles are congruent.
• If angles are not congruent, then the measures of the angles are not equal.
• If the measures of the angles are not equal, then the angles are not congruent.
• If the angles are not congruent, then the measure of the angles are equal.

What is the converse of the following statement?
If it is Saturday, then the school is closed

• If the school is closed, then it is Saturday.
• If it is not Saturday, then the school is not closed.
• If the school is not closed, then it is not Saturday.

Assuming these statements are true.

If I get good grades in high school, I will go to college.

I got all good grades.

Which is a valid conclusion using the law of detachment?

• I am not going to college.

• I am going to college.

• I am not getting good grades.

• I am a good student.

The given statements are true.

Statement: If you exercise regularly, then you have a healthy body

Statement: If you have a healthy body, then you have more energy.

Using the law of syllogism, which of the following is a valid conclusion?

• 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

This symbol, ∧, means?

• and
• or 
• not 
• implies

This symbol, ∨, means?

• and
• or
• not
• implies

Statement 1: If John does his homework, then he will pass the test.

Statement 2: If John passes the test, then he does his homework.

If Statement 1 is the conditional statement, then statement 2 is the -

• converse

• inverse

• contrapositive

• conditional

How is statement B related to statement A?

Statement A: If the two angles are not vertical, then the angles are not congruent.

Statement B: If two angles are vertical, then the angles are congruent.

• converse

• inverse

• contrapositive

• conditional

Statement: If there are clouds in the sky, then it is going to rain.

What is the contrapositive of this statement?

• If it is going to rain today, then there are clouds in the sky.

• If there are not clouds in the sky today, then it is not going to rain.

• If there are not clouds in the sky today, then it is going to rain.

• If it is not going to rain today, then there are no clouds in the sky.