
Directions: Answer these question pertaining to binary operations, as defined in each situation. Check your answer when finished. For questions #14, assume the set to be the real numbers.
1. 
Given: a b = a ^{2} b
What is the value of 3 4 ? 




2. 
Given: x y = 3x  4y
What is the value of 2 6 ? 




3. 
Given: r s = 2r + 3s
What is the value of 3 (4 5) ? 




4. 
Given: a b = a  b ^{2}
What is the value of (2 1) 3 ? 




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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