This example shows that we can reorder terms in any way we want.

In step 2 - 4, we show that:

(a ⋅ b) ⋅ (c ⋅ d) = (b ⋅ a) ⋅ (d ⋅ c)

And in step 6, we use the Swap Inner Terms theorem to claim that:

((b ⋅ a) ⋅ d) ⋅ c = ((b ⋅ d) ⋅ a) ⋅ c

Quiz (1 point)

• (a ⋅ b) ⋅ c = a ⋅ (b ⋅ c)
• a ⋅ b = b ⋅ a
• a ⋅ b = b ⋅ a
• a ⋅ (b ⋅ c) = (a ⋅ b) ⋅ c
• ((a ⋅ b) ⋅ c) ⋅ d = ((a ⋅ c) ⋅ b) ⋅ d

• if the following are true:

  • a = x
  • b = y

  then a ⋅ b = x ⋅ y

• if the following are true:

  • a = b
  • b = c
  • c = d
  • d = e

  then a = e

Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.

Step	Claim	Reason (optional)	Error Message (if any)
1
2
3
4
5
6
7
8
9
10

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