it is not enough to say \'yes\' or \'no for the questions posed. If your answer is eyes; explain why. If your answer is \'no; provide a

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. Suppose S = {a, b, c, d}. Let 

f = {(a, c), (b, c), (c, c), (d , c)} 

and 

g = {(a, a), (b, b), (c, c), (c, a), (c, d), (d, a)} . (a) Is f : S —> S a function? (h) Is g : S S a function? 

2. Consider the function B : {0,1}x N Z defined by 0(a, b) = a - 2a b + b. (a) Is 0 injective (one-to-one)? (h) Is 0 surjedive (onto)? 3. Suppose f and g are relations from X to Y. Prove or disprove: If f and g are functions, then f U g is a function. 

For problems 1 and 2, it is not enough to say 'yes' or 'no for the questions posed. If your answer is eyes; explain why. If your answer is 'no; provide a counterexample. 

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