Algebraic arguments often consist of a list of atatements. In a valid algebraic argument, each statement (after the premises) can be deduced from the previous statements. The following argument that 1 = 2 contains exactly one step that is not valid. Identify the step and explain why it is not valid. Let a=b Premise a2 = ab Multiply each side by a . a2 - b2 = ab - b2 Subtract b2 from each side. (a+b)(a-b) = b(a-b) Factor each side. a+b = b Divide each side by (a - b). b+b = b Substitute b for a . 2b = b Collect like terms. 2 = 1 Divide each side by b.
Algebraic arguments often consist of a list of atatements. In a valid algebraic argument, each statement (after the premises) can be deduced from the previous statements. The following argument that 1 = 2 contains exactly one step that is not valid. Identify the step and explain why it is not valid.
Let a=b Premise
a2 = ab Multiply each side by a .
a2 - b2 = ab - b2 Subtract b2 from each side.
(a+b)(a-b) = b(a-b) Factor each side.
a+b = b Divide each side by (a - b).
b+b = b Substitute b for a .
2b = b Collect like terms.
2 = 1 Divide each side by b.
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