Proof: Distributive Property Variation 3
Let's prove the following theorem:
(a + b) ⋅ c = (a ⋅ c) + (b ⋅ c)
Proof:
# | Claim | Reason |
---|---|---|
1 | (a + b) ⋅ c = (c ⋅ a) + (c ⋅ b) | (a + b) ⋅ c = (c ⋅ a) + (c ⋅ b) |
2 | c ⋅ a = a ⋅ c | c ⋅ a = a ⋅ c |
3 | (a + b) ⋅ c = (a ⋅ c) + (c ⋅ b) | if (a + b) ⋅ c = (c ⋅ a) + (c ⋅ b) and c ⋅ a = a ⋅ c, then (a + b) ⋅ c = (a ⋅ c) + (c ⋅ b) |
4 | c ⋅ b = b ⋅ c | c ⋅ b = b ⋅ c |
5 | (a + b) ⋅ c = (a ⋅ c) + (b ⋅ c) | if (a + b) ⋅ c = (a ⋅ c) + (c ⋅ b) and c ⋅ b = b ⋅ c, then (a + b) ⋅ c = (a ⋅ c) + (b ⋅ c) |
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