Question 1

If

n(A) = 3

and the set

A 	imes B

contains the elements

(1, x), (2, y),

and

(3, x)

, which of the following could be the set

B

if we know

n(A 	imes B) = 6

and

x 
e y

?

Accepted Answer

{x, y}

Answer

{x}

Answer

{x, y, z}

Answer

{1, 2, 3}

Question 2

Given two sets

n(A) = 3

and

A 	imes B

, let

(1, x), (2, y),

. How many subsets does the Cartesian product

(3, x)

have?

Accepted Answer

64

Answer

32

Answer

12

Answer

6

Question 3

If the set

n(A) = 3

contains 3 elements, how many elements are common to the sets

A 	imes B

and

(1, x), (2, y),

?

Accepted Answer

9

Answer

0

Answer

6

Answer

3

Question 4

If the set

n(A) = 3

has

A 	imes B

elements and the set

(1, x), (2, y),

has

(3, x)

elements, what is the total number of relations that can be defined from

B

to

n(A 	imes B) = 6

?

Accepted Answer

Answer

Answer

Answer

Question 5

If the Cartesian product

n(A) = 3

has 9 elements, and among these elements are found

A 	imes B

and

(1, x), (2, y),

, what are the remaining elements of the set

(3, x)

?

Accepted Answer

Answer

Answer

Answer

Question 6

If the set

n(A) = 3

has 2 elements and the set

A 	imes B

has 3 elements, what is the total number of non-empty relations that can be defined from

(1, x), (2, y),

to

(3, x)

?

Accepted Answer

63

Answer

31

Answer

64

Answer

6

Question 7

Which of the following statements regarding the Cartesian product is false for non-empty sets

n(A) = 3

and

A 	imes B

?

Accepted Answer

2^{pq}

in all cases

Answer

If

n(A) = 3

and

A 	imes B

, then

(1, x), (2, y),

Answer

Answer

Question 8

If the sets

n(A) = 3

and

A 	imes B

satisfy

(1, x), (2, y),

, which of the following statements must be true for any non-empty set

(3, x)

?

Accepted Answer

<math>(A 	imes C) \subseteq (B 	imes C)</math>

Answer

Answer

<math>(C 	imes A) \subseteq (A 	imes B)</math>

Answer

Question 9

If

n(A) = 3

and

A 	imes B

, what is the intersection of the sets

(1, x), (2, y),

and

(3, x)

?

Accepted Answer

{(3, 3)}

Answer

{(3, 3), (4, 4)}

Answer

Empty set

Answer

{(1, 3), (2, 3), (3, 3), (3, 4)}

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