1 20 what is the cardinality of each of these sets c d 2 let a b and c 5346358

February 4, 2021/in Business Homework Help Online /by Joseph

1 20. What is the cardinality of each of these sets?

c) {∅,{∅}}

d) {∅,{∅},{∅,{∅}}}

2 Let A, B, and C be sets. Show that

d) (A − C) ∩ (C − B) = ∅.

e) (B − A) ∪ (C − A) = (B ∪ C) − A.

3 Find f ◦ g and g ◦ f , where f (x) = x2 + 1 and g(x) = x + 2, are functions from R to R.

4 Suppose L = {a, b, c, d} and a function f : L → L is defined as follows:

f(a) = d, f(b) = b, f(c) = c, f(d) = d

Now, answer the following questions: [2 + 2 = 4 points]

a. Is f one-to-one? Explain your answer. [Do not just write Yes/No. Explanation required.]

b. Is f onto? Justify your answer. [Do not just write Yes/No. Explanation required.]

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