Question

Exercise 9.

In the questions below you can describe the relations/functions
either by drawing a diagram, by a formula, or by listing the
ordered pairs. Explain your solutions.

(i) Give an example of two sets A and B and a relation R from A to
B which is not a function.

(ii) [hard] Find a set A, |A| = 4 and deﬁne a bijective function
between A and P(A)? If such a set doesn’t exist give a reason.

Exercise 11. (i) Give an example of a function f : N → N which is total and injective, but not surjective. If such a function doesn’t exist, give a reason. Deﬁne the inverse function of the function f. If such a function doesn’t exist, give a reason. (ii) Give an example of a function f : N→N which is partial, injective, and surjective. If such a function doesn’t exist, give a reason.

Answer #1

Relations and Functions
Usual symbols for the above are;
Relations: R1, R2, S, T, etc
Functions: f, g, h, etc. But remember a function is a special
kind of relation so it might turn out that a Relation, R, is a
function, too.
Relations
To understand the symbolism better, let’s say the domain of a
relation, R, is A = { a, b , c} and the Codomain is B = {
1,2,3,4}.
Here is the relation: a R 1, ...

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Incentive Systems
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Please answer the following Case
analysis questions
1-How is New Balance performing compared to its primary rivals?
How will the acquisition of Reebok by Adidas impact the structure
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2- What issues does New Balance management need to address?
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What does New Balance need to do to continue to be successful?
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