Boot Camp Day 4: Logic

Classify each related conditional statement, based on the conditional statement "If I study, then I will pass the final exam."

a. I will pass the final exam if and only if I study.

b. If I do not study, then I will not pass the final exam.

c. If I pass the final exam, then I studied.

d. If I do not pass the final exam, then I did not study

• a. biconditional

  b. inverse

  c. converse

  d. contrapositive

• a. contrapositive

  b. converse

  c. inverse

  d. biconditional

• a. converse

  b. inverse

  c. biconditional

  d. contrapositive

• a. inverse

  b. biconditional

  c. contrapositive

  d. converse

Rewrite the conditional statement in if-then form. The measures of complementary angles sum to 90°

• The measures of two angles sum to 90 if and only if they are complementary.

• If two angles are complementary, then their measures sum to 90.

• If two angles are not complementary, then their measures do not sum to 90.

• If their measure sum to 90, then they are not complementary.

Tags

CCSS.7.G.B.5

What is the inverse of the conditional statement?

Conditional Statement: If a polygon is regular, then its sides are congruent.

• If a polygon’s sides are congruent, then it is regular.

• If a polygon is not regular, then its sides are not congruent.

• If a polygon’s sides are not congruent, then it is not regular.

• A polygon is regular if and only if its sides are congruent.

Identify the contrapositive of the given statement.

Given Statement: If two angles form a linear pair, then the angles are supplementary.

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

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

• Two angles form a linear pair if and only if the angles are supplementary.

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

Write the negation of the statement:

The dog is not a Labrador retriever.

• The dog is a Labrador retriever.

• The dog is a Hound.

• The dog is not a Lab.

• The dog is not a Hound.

Tags

CCSS.RI.8.7

CCSS.RI.9-10.7

CCSS.RL.11-12.7

CCSS.RL.8.7

CCSS.RL.9-10.7

Decide whether the statement about the diagram is true. Explain your answer using the definitions you have learned.

m∠2 + m∠3 = 180∘

• true; The angles sum to 180º because they are not complementary.

• true; If angles form a linear pair, then the sum of the measures of their angles is 180º.

• false; The angles are supplementary, so their measures should sum to 90º.

• false; By definition, adjacent angles can sum to any measure between 135º and 180º.

Tags

CCSS.7.G.B.5

Rewrite the definition as a biconditional statement.

The midpoint of a segment is the point that divides the segment into two congruent segments.

• If it is a midpoint of a segment, then it divides the segment into two congruent segments.

• If it is not a midpoint of a segment, then it does not divide the segment into two congruent segments.

• The point is a midpoint of a segment if and only if it divides the segment into two congruent segments.

• If it divides the segment into two congruent segments, then it is a midpoint of a segment.

Tags

CCSS.HSG.CO.C.10

• x = 4

• x = 2

• x = 4

• x = -2

Tags

CCSS.HSA.REI.B.4

Select the counterexample that shows that the conjecture is false.

Conjecture: A line s divides line MN into two line segments. So, the line s is the segment bisector of line MN.

• If another line also divides line MN, then line s is not the only segment bisector of line MN.

• Line s must intersect line MN at a right angle in order to be the segment bisector of line MN.

• If line s intersects line MN anywhere besides the midpoint, it is not the segment bisector of line MN.

• If line s intersects line MN at the midpoint, it is the perpendicular bisector of line MN.

Select the counterexample that shows that the conjecture is false.

Conjecture: If two angles are supplements of each other, then one of the angles must be acute.

• Both angles could be right angles.

• When one angle is 135º, the supplement is not acute.

• Both angles could be straight angles.

• When one angle is 25º, the supplement is not acute.

Tags

CCSS.7.G.B.5