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Logic and Proof

Logic and Proof

Logic and Proof: Equality and Congruence for All! True or False

1. What property of equality would you use to solve for x in the equation 5x = 15?Symmetry
2. Which is an example of the symmetric property of equality?If A = B and B = C, then A = C
3. Which of these is not a property of equality (and therefore congruence)?Transitivity
4. Which property lets us simplify the equation (10 – 5)2x – (10 – 5) = 0 to 52x – 5 = 0?Reflexive Property
5. We are given that A = B and C = D. What would make the statement A/C = B/D untrue?D = 0
6. 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 = -6

7. 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

8. 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?

9. 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?

10. 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 = -9


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