Reference no: EM132185835

1. Suppose f:Z→ Z, with defined by f(x) = 3x2 + 3. Note that both the domain and the target are equal to Z, the set of all integers.

Explain using the definition of an onto function why the function f is or is not onto.

2. Consider the relation R on the set S = {1, 2, 3, 4} defined by

R = { (1,1), (1,3), (2, 1), (2,2), (3,3), (3, 4), (4,1), (4,3)}.

?a. Explain why R is or is not symmetric.

?b. Explain why R is or is not transitive.

3. Suppose A = {1, 2, 3, 4}. Let S and R be relations on A defined as follows:

?S = { (1, 1), (1, 3), (2, 3), (2,4), (3, 4), (4,1) }

?R = { (1, 4), (2, 2), (3, 2), (4, 2) }

?Write the set of ordered pairs that is S ο R.