Unit 3 Flashcards
What is the negation of m∠1 + m∠2 = 90°?
m∠1 + m∠2 ≠ 90°
What is the negation of x is purple?
x is not purple
What is the negation of x + 7 ≠ 5?
x + 7 = 5
What is the negation of ∠1 & ∠2 are not complementary?
Ð1 & Ð2 are complementary
What is the negation of x – 5 ≤ 7?
x – 5 > 7
What is the negation of m∠1 < m∠2?
m∠1 ≥ m∠2
What letters are used for hypothesis and conclusion?
p - hypothesis q - conclusion
What are the three ingredients needed for a good counterexample?
- Must work for hypothesis 2. Must not work for conclusion 3. Must be specific
For any conditional statement, how do you find the converse?
Switch the hypothesis and conclusion
For any conditional statement, how do you find the inverse?
Negate the hypothesis and conclusion
For any conditional statement, how do you find the contrapositive?
Switch and negate the hypothesis and conclusion
What words do we use to write any biconditional?
If and only if (iff)
How do you determine the truth value of any biconditional?
If both conditionals are true then the biconditional is true - if either conditional is false, then the biconditional is false
What does it mean for statements to be “logically equivalent”?
They have the same truth value, justification if true, and counterexample if false
How do you write a logically equivalent statement to any conditional statement?
Switch and negate the hypothesis and conclusion
Which of the four types of conditional statements are logically equivalent?
Conditional & Contrapositive, Converse & Inverse
What is the difference between multiplication and distribution?
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
What is the difference between addition and subtraction?
Nothing
What is the difference between multiplication and division?
Nothing
Explain the reflexive property of equality
Any number equals itself
Explain the symmetric property of equality
The property that justifies switching sides of an equation
Explain the transitive property of equality
If 2 numbers equal the same 3rd number, then they also equal each other
Explain the substitution property of equality
The property that justifies substituting a value for an equal value
Explain the reflexive property of congruence
Any figure is congruent to itself
Explain the symmetric property of congruence
The property that justifies switching sides of a congruency
Explain the transitive property of congruence
If 2 figures are congruent to the same 3rd figure, then they are also congruent to each other
Explain the substitution property of congruence
There is no substitution property of congruence
If ∠1 is supplementary to Ð3, and Ð2 is supplementary to Ð3, then what is true?
Ð1 ≅ Ð2
What is the justification for “If Ð1 is supplementary to Ð3, and Ð2 is supplementary to Ð3, then what is true”?
SCAC
If ÐK is complementary to ÐM, and ÐN is complementary to ÐK, then what is true?
ÐM ≅ ÐN
What is the justification for “If ÐK is complementary to ÐM, and ÐN is complementary to ÐK, then what is true”?
CCAC
Write the converse of “If x = 9, then x < 25”, and find the truth value.
If x < 25, then x = 9. False, x = 10
Write the inverse of “If x = 9, then x < 25”, and find the truth value.
If x ≠ 9, then x ≥ 25. False x = 10
Write the contrapositive of “If x = 9, then x < 25”, and find the truth value.
If x ≥ 25, then x ≠ 9. True
Write the related biconditional for “If x = 9, then x < 25”, and find the truth value.
x = 9 iff x < 25 or x < 25 iff x = 9. False x = 10
If the inverse of a conditional is “If n = 10, then n ≠ 5,” give the converse of the original conditional statement
If n = 5, then n ≠ 10
