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 5*x* = 15?

Symmetry

Transitivity

Substitution

Division

Reflexive

Q. Which is an example of the symmetric property of equality?

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?

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* = 7

2*x* = 8

2*x* + 1 = 7

2*x* = -6

2*x* = -8

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 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?