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Logic and Proof

Logic and Proof

Logic and Proof: Equality and Congruence for All! Quiz

Think you’ve got your head wrapped around Logic and Proof? Put your knowledge to the test. Good luck — the Stickman is counting on you!
Q. What property of equality would you use to solve for x in the equation 5x = 15?


Symmetry
Transitivity
Substitution
Division
Reflexive
Q. Which is an example of the symmetric property of equality?


A = A
If A = B and B = C, then A = C
If A = B, then B = A
If A = B, B can be used for all A
None of the above
Q. Which of these is not a property of equality (and therefore congruence)?


Symmetry
Reflexivity
Transitivity
Substitution
Inversion
Q. Which property lets us simplify the equation (10 – 5)2x – (10 – 5) = 0 to 52x – 5 = 0?


Transitive Property
Addition Property
Subtraction Property
Reflexive Property
Substitution Property
Q. We are given that A = B and C = D. What would make the statement A/C = B/D untrue?


A = 0
B = C
C = D
D = 0
Nothing, that statement is always true
Q. Fill in the missing statements in the following proof that if 2x + 7 = 1 and yx – 1 = 2, then y = -9.

StatementsReasons
1. 2x + 7 = 1Given
2. yx – 1 = 2Given
3. ?Subtract 7 from both sides of (1)
4. ?Divide (3) by 2
5. ?Substitute (4) into (2)
6. ?Add 1 to both sides of (5)
7. ?Multiply (6) by –3

Which of the following fits best for statement 3?



2x = 7
2x = 8
2x + 1 = 7
2x = -6
2x = -8
Q. Fill in the missing statements in the following proof that if 2x + 7 = 1 and yx – 1 = 2, then y = -9.

StatementsReasons
1. 2x + 7 = 1Given
2. yx – 1 = 2Given
3. ?Subtract 7 from both sides of (1)
4. ?Divide (3) by 2
5. ?Substitute (4) into (2)
6. ?Add 1 to both sides of (5)
7. ?Multiply (6) by –3

Which of the following fits best for statement 4?



x = 3
x = -3
x = 6
x = -6
x = 4
Q. Fill in the missing statements in the following proof that if 2x + 7 = 1 and yx – 1 = 2, then y = -9.

StatementsReasons
1. 2x + 7 = 1Given
2. yx – 1 = 2Given
3. ?Subtract 7 from both sides of (1)
4. ?Divide (3) by 2
5. ?Substitute (4) into (2)
6. ?Add 1 to both sides of (5)
7. ?Multiply (6) by –3

Which of the following fits best for statement 5?



Q. Fill in the missing statements in the following proof that if 2x + 7 = 1 and yx – 1 = 2, then y = -9.

StatementsReasons
1. 2x + 7 = 1Given
2. yx – 1 = 2Given
3. ?Subtract 7 from both sides of (1)
4. ?Divide (3) by 2
5. ?Substitute (4) into (2)
6. ?Add 1 to both sides of (5)
7. ?Multiply (6) by –3

Which of the following fits best for statement 6?



Q. Fill in the missing statements in the following proof that if 2x + 7 = 1 and yx – 1 = 2, then y = -9.

StatementsReasons
1. 2x + 7 = 1Given
2. yx – 1 = 2Given
3. ?Subtract 7 from both sides of (1)
4. ?Divide (3) by 2
5. ?Substitute (4) into (2)
6. ?Add 1 to both sides of (5)
7. ?Multiply (6) by –3

Which of the following fits best for statement 7?



x = 6
y = 9
y = -9
x = -6
x = -9
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