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.

Tags

CCSS.8.G.A.2

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.