Unit 3

Question 1

What is the negation of m∠1 + m∠2 = 90°?

Answer 1

m∠1 + m∠2 ≠ 90°

Question 2

What is the negation of x is purple?

Answer 2

x is not purple

Question 3

What is the negation of x + 7 ≠ 5?

Answer 3

x + 7 = 5

Question 4

What is the negation of ∠1 & ∠2 are not complementary?

Answer 4

Ð1 & Ð2 are complementary

Question 5

What is the negation of x ­– 5 ≤ 7?

Answer 5

x – 5 > 7

Question 6

What is the negation of m∠1 < m∠2?

Answer 6

m∠1 ≥ m∠2

Question 7

What letters are used for hypothesis and conclusion?

Answer 7

p - hypothesis q - conclusion

Question 8

What are the three ingredients needed for a good counterexample?

Answer 8

1. Must work for hypothesis 2. Must not work for conclusion 3. Must be specific

Question 9

For any conditional statement, how do you find the converse?

Answer 9

Switch the hypothesis and conclusion

Question 10

For any conditional statement, how do you find the inverse?

Answer 10

Negate the hypothesis and conclusion

Question 11

For any conditional statement, how do you find the contrapositive?

Answer 11

Switch and negate the hypothesis and conclusion

Question 12

What words do we use to write any biconditional?

Answer 12

If and only if (iff)

Question 13

How do you determine the truth value of any biconditional?

Answer 13

If both conditionals are true then the biconditional is true - if either conditional is false, then the biconditional is false

Question 14

What does it mean for statements to be “logically equivalent”?

Answer 14

They have the same truth value, justification if true, and counterexample if false

Question 15

How do you write a logically equivalent statement to any conditional statement?

Answer 15

Switch and negate the hypothesis and conclusion

Question 16

Which of the four types of conditional statements are logically equivalent?

Answer 16

Conditional & Contrapositive, Converse & Inverse

Question 17

What is the difference between multiplication and distribution?

Answer 17

Multiplication occurs when you multiply only 2 numbers, while distribution occurs when you multiply a number through a quantity of 2 or more terms linked by addition or subtraction

Question 18

What is the difference between addition and subtraction?

Answer 18

Nothing

Question 19

What is the difference between multiplication and division?

Answer 19

Nothing

Question 20

Explain the reflexive property of equality

Answer 20

Any number equals itself

Question 21

Explain the symmetric property of equality

Answer 21

The property that justifies switching sides of an equation

Question 22

Explain the transitive property of equality

Answer 22

If 2 numbers equal the same 3rd number, then they also equal each other

Question 23

Explain the substitution property of equality

Answer 23

The property that justifies substituting a value for an equal value

Question 24

Explain the reflexive property of congruence

Answer 24

Any figure is congruent to itself

Question 25

Explain the symmetric property of congruence

Answer 25

The property that justifies switching sides of a congruency

Question 26

Explain the transitive property of congruence

Answer 26

If 2 figures are congruent to the same 3rd figure, then they are also congruent to each other

Question 27

Explain the substitution property of congruence

Answer 27

There is no substitution property of congruence

Question 28

If ∠1 is supplementary to Ð3, and Ð2 is supplementary to Ð3, then what is true?

Answer 28

Ð1 ≅ Ð2

Question 29

What is the justification for "If Ð1 is supplementary to Ð3, and Ð2 is supplementary to Ð3, then what is true"?

Answer 29

SCAC

Question 30

If ÐK is complementary to ÐM, and ÐN is complementary to ÐK, then what is true?

Answer 30

ÐM ≅ ÐN

Question 31

What is the justification for "If ÐK is complementary to ÐM, and ÐN is complementary to ÐK, then what is true"?

Answer 31

CCAC

Question 32

Write the converse of "If x = 9, then x < 25", and find the truth value.

Answer 32

If x < 25, then x = 9. False, x = 10

Question 33

Write the inverse of "If x = 9, then x < 25", and find the truth value.

Answer 33

If x ≠ 9, then x ≥ 25. False x = 10

Question 34

Write the contrapositive of "If x = 9, then x < 25", and find the truth value.

Answer 34

If x ≥ 25, then x ≠ 9. True

Question 35

Write the related biconditional for "If x = 9, then x < 25", and find the truth value.

Answer 35

x = 9 iff x < 25 or x < 25 iff x = 9. False x = 10

Question 36

If the inverse of a conditional is "If n = 10, then n ≠ 5," give the converse of the original conditional statement

Answer 36

If n = 5, then n ≠ 10