SOL Review Quiz 1 G.1 Logic

Let p represent

Brent works this summer.

Let q represent

Brent takes a vacation.

Symbolically represent the following argument.

If Brent works this summer, then he will not take a vacation.

Brent takes a vacation.

Therefore, Brent does not work this summer.

• p→q

  ∼q

  ∴∼p

• p→q

  p

  ∴q

• p→∼q

  q

  ∴∼p

• q→p

  ∼q

  ∴p

Given the original statement, "If you are nice to your sister, then you will not get into trouble." Which of the following represents the converse of this statement?

• If you don't get into trouble, then you are nice to your sister.

• If you are not nice to your sister, then you will not get into trouble.

• If you are mean to your sister, then you will get into trouble.

• You are not nice to your sister if and only if you do not get into trouble.

• If you get into trouble, then you were not nice to your sister.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Given the original statement, “If you are nice to your sister, then you will not get into trouble.”, which statement represents the inverse of the statement?

• If you get into trouble, then you were not nice to your sister.

• If you are not nice to your sister, then you will get into trouble.

• If you are not nice to your sister, then you will not get into trouble.

• If you don't get into trouble, then you are nice to your sister.

• You are nice to your sister if and only if you do not get into trouble.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Given the original statement, "If you are nice to your sister, then you will not get into trouble." Which of the following represents the contrapositive of this statement?

• If you don't get into trouble, then you are nice to your sister.

• If you are not nice to your sister, then you will not get into trouble.

• If you are not nice to your sister, then you will not get into trouble.

• If you get into trouble, then you were not nice to your sister.

• If you were mean to your sister, then you will not get into trouble.

Given the original statement, "If you are nice to your sister, then you will not get into trouble." Which of the following represents the biconditional of this statement?

• If you don't get into trouble, then you are nice to your sister.

• If you are not nice to your sister, then you will not get into trouble.

• If you are mean to your sister, then you will get into trouble.

• You are nice to your sister if and only if you do not get into trouble.

• If you get into trouble, then you were not nice to your sister.

Give a counterexample to the following statement:

If n is an integer, then n² > n.

• -2

• -1

• 1

• 2

Which set of statements represents a valid argument?

• If a road is icy, then diriving conditions are hazardous.

  Driving conditions are hazardous.

  Therefore, the road is icy.

• If there is lighning, then it is not safe to be out in the open.

  Marla sees lightning from the soccer field.

  Therefore, it is not safe for Marla to be out in the open.

• If the electric power is out, then the refrigerator does not work.

  If the refrigerator does not work, then the food is spoiled.

  Therefore, if the food is spoiled, then the electric power is out.

• If John studies, then he will pass the Geometry test.

  If John passes the Geometry test, he will not be grounded.

  Therefore, if John is grounded, then he will study.