NOTE: Points (+ x) Recall that in Set theory, sets are unordered. {a, b, c } == {b, c, a }

(+5) Assume

A == the set of prime numbers less than 10

B == the set of odd integers less than 10

C == the set of even integers less than 10

How many of the following statements are true

A is a subset of B B is a subset of A A is a subset of C

C is a subset of A B is a subset of C C is a subset of A

a. 0

b. 1.

c. 2.

d. 3

(+5) A = {a, b, c, d } How many subsets does A have ?

a. 16

b. 4.

c. 8

d. 32

3(+5) If A is a set with |A| = 6 then what is |P(A)| ?

a. 64

b. 32

c. 128

d. None of the above

4(+5) If A is a set with A = { 2, 5, 7, 11 } then what is |(A xA) U A)|

a. 20

b. 16

c. 32

d. None of the above

5 (+5) How many numbers between 1 and 100 (inclusive) are divisible by 4 or 9

HINT:

There are 25 numbers divisible by 4 between 1 and 100, and 11 numbers divisible by 9 between 1and 100. So, you might think there are 25 + 11 = 36 numbers divisible by 4 and 9?

a. 32

b. 30

c. 34

d. None of the above

6(+5) If A = {a,b,c} and B = { 1, 2 } then how many relations with 3 tuples are possible using the Cartesian product A x B

₆C₆

₆C₃

₁₆C₃

None of the above

7 (+5) If A = {a, b, c} the Power set P (A) contains the following

{ {}, {a}, {b}, {c}, {a,c}, {a,b} {b,c}, {a,b,c} }

{ {a}, {b}, {c}, {a,c}, {a,b} {b,c}, {a,b,c} }

{ {a,b,c} }

None of the above

8(+5)What is the Cartesian product of A = {1, 2} and B = {a, b}?

b { (1, 1), (2, 2), (a, a), (b, b) } c { (1, a), (2, a), (1, b), (2, b) } d { (1, 1), (a, a), (2, a), (1, b)}

9 (+5) Given the following sets A = {1, 2} and B = {a, b}, which of the following are functions?

b { (1, a), (2, a), (b, b) } c { (1, a), (2, a), (1, b) } d None of these