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Q15 – 6 points Define a function f : Z → Z by the rule f(n) = 2n , for every integer n. Is f an onto function? Is f a one-to-one function? Prove using the definitions of onto and one-to-one.

Q2 – 9 points Let G = {1, 2, 3} and  H = {5, 6, 7} and define a relation R from G to H as follows: For every (x, y) ∈ G × H,  (x, y) ∈ R  means that  (x – y)/2  is an integer. Is 3 R 6? Is (2, 7) ∈ R? Write R  as a set of ordered pairs.  

Q13 – 6 points Define a function F : Z × Z → Z × Z as follows: F(x, y) = (y−1, 3−x) for all (x, y) in Z × Z.  Find F(0, 0) and F(3, 4).

Q6 – 8 points Write a proof for the following statement: For all sets A and B, if A ⊆ B, then A ⊆ A ∩ B.

At lower quantities on the demand curve

I certify that I received no unauthorized aid on this exam and completed it fully on my own.  I received no assistance from any other person.

List four Agents of Socialization that impact individuals.

A ______ would be most interested in the relationship and nature of day-to- day exchanges between the two groups.

The concept “reference groups” can be defined as:

Which social paradigm would compare society to a human body?