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Given that a and b are integers such that a = b + 1,
Prove: 1 = 0
1. a = b + 1 (Given)
2. (a-b)a = (a-b)(b+1) (Multiplication Prop. of =)
3. a2 – ab = ab + a – b2 – b (Distributive Property)
4. a2 – ab -a = ab + a -a – b2 – b (Subtraction Prop. of =)
5. a(a – b – 1) = b(a – b – 1) (Distributive Property)
6. a = b (Division Property of = )
7. b + 1 = b (Transitive Property of = (Steps 1, 7) )
8. Therefore, 1 = 0 (Subtraction Prop. of =)
Prove: 1 = 0
1. a = b + 1 (Given)
2. (a-b)a = (a-b)(b+1) (Multiplication Prop. of =)
3. a2 – ab = ab + a – b2 – b (Distributive Property)
4. a2 – ab -a = ab + a -a – b2 – b (Subtraction Prop. of =)
5. a(a – b – 1) = b(a – b – 1) (Distributive Property)
6. a = b (Division Property of = )
7. b + 1 = b (Transitive Property of = (Steps 1, 7) )
8. Therefore, 1 = 0 (Subtraction Prop. of =)