Exploring Binary Operations Terms of Use    Contact Person: Donna Roberts
Directions: Answer these question pertaining to binary operations, as defined in each situation. Check your answer when finished. For questions #1-4, assume the set to be the real numbers.

1.
Given: a b = a2- b
What is the value of 3 4 ?
Choose:
 2 5 12 13

2.
Given: x y = |3x - 4y|
What is the value of 2 6 ?
Choose:
 -18 -14 14 18

3.
Given: r s = 2r + 3s
What is the value of 3 (4 5) ?
Choose:
 23 43 75 76

4.
Given: a b = a - b2
What is the value of (2 1) 3 ?
Choose:
 1 -6 -8 -12

 5. Operation is defined on the set { D, O, G, S } as shown in the table below: a.  What is the value of O G ? b.  Is this operation commutative? Explain. c.  What is the identity element? Justify your answer. d.  Find the inverse of each element. e.  True or false:       (D G) S = D (G S)

 6. Operation is defined on the set { m, a, t, h } as shown in the table below: a.  What is the value of m a ? b.  Is this operation commutative? Explain. c.  What is the identity element? Justify your answer. d.  Find the inverse of each element. e.  True or false:          m (a t) = (m a) t

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