Quiz (1 point)

• a = a ⋅ 1
• 4 / 4 = 1
• (a ⋅ b) + (a ⋅ c) = a ⋅ (b + c)
• (4 / 4) + ((-1) / 4) = 3 / 4
• a + (b ⋅ ((-1) / c)) = a - (b / c)
• a ⋅ b = b ⋅ a

• if a = b, then c ⋅ a = c ⋅ b

• if the following are true:

  • a = c
  • b = c

  then a = b

• if the following are true:

  • a = b ⋅ c
  • c = d

  then a = b ⋅ d

• if the following are true:

  • a + b = c
  • d = a

  then d + b = c

• if the following are true:

  • a = b
  • a = c

  then b = c

• if the following are true:

  • a = b
  • b = c

  then a = c

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.