Unit 3: Logic Test Review

Which of the following is the inverse of the conditional: "If two angles are vertical angles, then they are congruent."?

• If two angles are congruent, then they are vertical angles.

• If two angles are not congruent, then they are not vertical angles.

• If two angles are not vertical angles, then they are not congruent.

• If two angles are not vertical angles, then they are congruent.

Tags

CCSS.HSG.CO.B.7

Given the converse, "If angles are a linear pair, then they are supplementary," what is the conditional?

• If two angles are supplementary, then they form a linear pair.

• If two angles are not a linear pair, then they are not supplementary.

• If two angles are not supplementary, then they do not form a linear pair.

• If two angles are a linear pair, then they are not supplementary.

Tags

CCSS.8.G.A.5

"If two sides of a triangle are congruent, then the angles opposite those sides are congruent."

Which of the following is the statement written as a biconditional?

• If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

• Two angles of a triangle are congruent if and only if the sides opposite those angles are congruent.

• Two sides of a triangle are congruent if the angles opposite those sides are congruent.

• If two sides of a triangle are not congruent, then the angles opposite those sides are not congruent.

Tags

CCSS.HSG.CO.C.9

Which of the following is the contrapositive of the conditional?

"Perpendicular lines intersect to form four right angles."

• If two lines are perpendicular, then they intersect to form four right angles.

• If two lines do not intersect to form four right angles, then they are not perpendicular.

• If two lines are not perpendicular, then they do not intersect to form four right angles.

• If two lines intersect to form four right angles, then they are perpendicular.

If the inverse of the conditional is, "If you do not live in Virginia, then you live in Richmond," then what is the contrapositive of the same statement?

• If you live in Virginia, then you do not live in Richmond.

• If you live in Richmond, then you do not live in Virginia.

• If you do not live in Richmond, then you live in Virginia.

• If you do not live in Virginia, then you live in Richmond.

Tags

CCSS.RL.11-12.1

CCSS.RL.9-10.1

CCSS.RI.8.1

CCSS.RL.8.1

CCSS.RI.8.8

Your original statement is, "If a shape has four sides of equal length, then it must be a square."

It is transformed into "If a shape is a square, then it must have four equal sides."

What type of logic statement is the second, if the first is your conditional?

• Converse

• Inverse

• Contrapositive

Let p = A triangle has 3 sides.

q = A quadrilateral has 4 sides.

Which of the following symbolic forms represents, "If a quadrilateral doesn't have 4 sides, then a triangle doesn't have 3 sides."

• p -> q

• q -> p

• ~p -> ~q

• ~q -> ~p

Tags

CCSS.HSS.CP.A.1

Which of the following symbolic forms is the converse of ~p -> q?

• q -> ~p

• q -> p

• ~q -> ~p

• p -> ~q

Let p = It is sunny outside

q = I will go to the beach

Which statement represents q -> ~p?

• If it is not sunny outside, then I will go to the beach.

• If I go to the beach, then it is not sunny outside.

• If it is sunny outside, then I will not go to the beach.

• If I do not go to the beach, then it is sunny outside.

Tags

CCSS.7.SP.C.8B

Let p = Tom goes fishing.

q = He brings a pole.

What is the symbolic representation of the following:

"If Tom goes fishing, then he brings a pole.

Tom does not go fishing.

Therefore, Tom does not bring a pole."

• p -> q

  p

  ∴~q

• ~p -> ~q

  ~p

  ∴ ~q

• ~p -> q

  ~p

  ∴ q

• p -> q

  ~p

  ∴ ~q