# Proofs Exercises

### Example 1

What is the reason for statement 7?

Given: A = B, B = C, X = Y, Y = Z, H = G, G ≠ 0

Prove:

 Statements Reasons 1. A = B Given 2. B = C Given 3. X = Y Given 4. Y = Z Given 5. H = G Given 6. G ≠ 0 Given 7. A = C ?

### Example 2

What is the reason for statement 8?

Given: A = B, B = C, X = Y, Y = Z, H = G, G ≠ 0

Prove:

 Statements Reasons 1. A = B Given 2. B = C Given 3. X = Y Given 4. Y = Z Given 5. H = G Given 6. G ≠ 0 Given 7. A = C Transitive Property (1 and 2) 8. H ≠ 0 ?

### Example 3

What is the reason for statement 9?

Given: A = B, B = C, X = Y, Y = Z, H = G, G ≠ 0

Prove:

 Statements Reasons 1. A = B Given 2. B = C Given 3. X = Y Given 4. Y = Z Given 5. H = G Given 6. G ≠ 0 Given 7. A = C Transitive Property (1 and 2) 8. H ≠ 0 Substitution Property (5 and 6) 9. AB = BB ?

### Example 4

What is statement 11 given its reason?

Given: A = B, B = C, X = Y, Y = Z, H = G, G ≠ 0

Prove:

 Statements Reasons 1. A = B Given 2. B = C Given 3. X = Y Given 4. Y = Z Given 5. H = G Given 6. G ≠ 0 Given 7. A = C Transitive Property (1 and 2) 8. H ≠ 0 Substitution Property (5 and 6) 9. AB = BB Multiplication Property (1) 10. AB = CB Substitution Property (9 and 2) 11. ? Division Property (10 and 6)

### Example 5

What is statement 12 given its reason?

Given: A = B, B = C, X = Y, Y = Z, H = G, G ≠ 0

Prove:

 Statements Reasons 1. A = B Given 2. B = C Given 3. X = Y Given 4. Y = Z Given 5. H = G Given 6. G ≠ 0 Given 7. A = C Transitive Property (1 and 2) 8. H ≠ 0 Substitution Property (5 and 6) 9. AB = BB Multiplication Property (1) 10. AB = CB Substitution Property (9 and 2) 11. Division Property (10 and 6) 12. ? Substitution Property (11 and 5)

### Example 6

What is statement 13 given its reason?

Given: A = B, B = C, X = Y, Y = Z, H = G, G ≠ 0

Prove:

 Statements Reasons 1. A = B Given 2. B = C Given 3. X = Y Given 4. Y = Z Given 5. H = G Given 6. G ≠ 0 Given 7. A = C Transitive Property (1 and 2) 8. H ≠ 0 Substitution Property (5 and 6) 9. AB = BB Multiplication Property (1) 10. AB = CB Substitution Property (9 and 2) 11. Division Property (10 and 6) 12. Substitution Property (11 and 5) 13. ? Multiplication Property (12)

### Example 7

What is the reason for statement 14?

Given: A = B, B = C, X = Y, Y = Z, H = G, G ≠ 0

Prove:

 Statements Reasons 1. A = B Given 2. B = C Given 3. X = Y Given 4. Y = Z Given 5. H = G Given 6. G ≠ 0 Given 7. A = C Transitive Property (1 and 2) 8. H ≠ 0 Substitution Property (5 and 6) 9. AB = BB Multiplication Property (1) 10. AB = CB Substitution Property (9 and 2) 11. Division Property (10 and 6) 12. Substitution Property (11 and 5) 13. Multiplication Property (12) 14. X = Z ?

### Example 8

What is the reason for statement 15?

Given: A = B, B = C, X = Y, Y = Z, H = G, G ≠ 0

Prove:

 Statements Reasons 1. A = B Given 2. B = C Given 3. X = Y Given 4. Y = Z Given 5. H = G Given 6. G ≠ 0 Given 7. A = C Transitive Property (1 and 2) 8. H ≠ 0 Substitution Property (5 and 6) 9. AB = BB Multiplication Property (1) 10. AB = CB Substitution Property (9 and 2) 11. Division Property (10 and 6) 12. Substitution Property (11 and 5) 13. Multiplication Property (12) 14. X = Z Transitive Property (3 and 4) 15. ?