Discrete Mathematics Answers

Read the instruction carefully .

Consider the Function f={1,2,3,4}->{1,2,3,4} given by f(n) =(1 2 3 4) (4 1 3 4)

a.find f(1)=

b.Find an element n in the domain such that f(n)=1

c.Find an element n of the domain such that f(n)=n

d.Find an element of the domain that is not range.=

The following functions all have {1,2,3,4,5} as both domain and codomain for each.determine whether it is (only) injective,(only) surjective, bijective or either injective nor surjective.

a. f=(1 2 3 4 5) (3 3 3 3 3)=

b.f=(1 2 3 4 5) (2 3 1 5 4)=

c.f(x)=6-x =

d. f(x)={x/2

(x+1)/2

if x is even

if x is odd=

The following function all have domain {1 2 3 4 5} and co domain { 1 2 3}. For each determine whether it is (only)injective,(only) surjective, bijective or either injective nor surjective.

V. LEARNING ACTIVITIES:

1. A function is __________+__________.

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2. The vertical line test says that a graph is a graph of a function if every vertical line passes through the graph ___________.

For exercises 3 through 6 answer either "True" or "False" and explain how you arrived at your conclusion.

3. The graph of a function can never have more than one y-intercept.

4. The graph of a function can never have more than one x-intercept.

5. Every line is the graph of a function.

6. Circles are never graphs of functions.

For exercises 7 - 10, a relation is given in the form of ordered pairs. Determine the domain, the range, state whether the relation is a function.

7. (1,2), (2,3), (3,4), (4,5), (7,7)

8. (-1,4), (0,5), (1,4), (2,3)

9. (0,2), (1,6), (1,5), (9,12), (10,11)

10. (-3,-1), (-1,-3), (0,5), (2,1)

Read the instruction carefully. Write your answer in the box.

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What is the truth values for the Compound Proposition:

(P =>Q) => R