1. (10p) For the given two real valued functions f(x) = 2x2 + 1 and g(x) = 2x + 1 find the composite functions f g and g f

State your answer in the standard polynomial form.

(a) f g (x) =

(b) g f (x) =

2. (12p) For a given set and a relation R on X, answer the following questions. Circle your choices.

(a) X = {1, 2, 3, 4, 5}, R = {(1,1), (2,2), (3,3), (4,4), (5,5), (1,2), (2,3),(1,3)}

I

Is R is reflexive? Yes No

Is R is symmetric? Yes No

Is R is anti-symmetric? Yes No

Is R is transitive? Yes No

Is R is a partial order? Yes No

Is R is an equivalence relation? Yes No

(b) X = {1, 2, 3, 4}, R = {(1,1), (2,2), (3,3), (1,2), (2,1)}

Is R is reflexive? Yes No

Is R is symmetric? Yes No

Is R is anti-symmetric? Yes No

Is R is transitive? Yes No

Is R is a partial order? Yes No

Is R is an equivalence relation? Yes No

3. (6p) For the given partition of set X, write the corresponding equivalence relation R.

X = {1, 2, 3, 4, 5, 6}, X1 = {1, 2, 3}, X2 = {4}, X3 = {5, 6}.

R =