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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 = a 2- b
What is the value of 3 4 ? |
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2. |
Given: x  y = |3x - 4y|
What is the value of 2 6 ? |
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3. |
Given: r  s = 2r + 3s
What is the value of 3 (4 5) ? |
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4. |
Given: a  b = a - b 2
What is the value of (2 1) 3 ? |
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| 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)
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| 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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