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# Logic and Proof

# Logic and Proof: Equality and Congruence for All! Quiz

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Logic and Proof**Q. What property of equality would you use to solve for

*x*in the equation 5*x*= 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 5^{2x}– 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 2

*x*+ 7 = 1 and^{y}⁄_{x}– 1 = 2, then*y*= -9.Statements | Reasons |

1. 2x + 7 = 1 | Given |

2. ^{y}⁄_{x} – 1 = 2 | Given |

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?

2

*x*= 72

*x*= 82

*x*+ 1 = 72

*x*= -62

*x*= -8Q. Fill in the missing statements in the following proof that if 2

*x*+ 7 = 1 and^{y}⁄_{x}– 1 = 2, then*y*= -9.Statements | Reasons |

1. 2x + 7 = 1 | Given |

2. ^{y}⁄_{x} – 1 = 2 | Given |

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 2

*x*+ 7 = 1 and^{y}⁄_{x}– 1 = 2, then*y*= -9.Statements | Reasons |

1. 2x + 7 = 1 | Given |

2. ^{y}⁄_{x} – 1 = 2 | Given |

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 2

*x*+ 7 = 1 and^{y}⁄_{x}– 1 = 2, then*y*= -9.Statements | Reasons |

1. 2x + 7 = 1 | Given |

2. ^{y}⁄_{x} – 1 = 2 | Given |

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 2

*x*+ 7 = 1 and^{y}⁄_{x}– 1 = 2, then*y*= -9.Statements | Reasons |

1. 2x + 7 = 1 | Given |

2. ^{y}⁄_{x} – 1 = 2 | Given |

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