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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics
8.1 Cartesian Product of Sets

If A and B are any two sets, the set of all possible ordered pairs (a,b) with a A and b B, is called the cartesian product of A and B and is denoted by A B. and it is read as A cross B.
The set builder form of A B is
A B = {(a,b)/a A and b B}
Observing the above relation we find the following points.
1. The ordered pair of A B, the first coordinate belongs to A while the second coordinate belongs to B.
2. A B B A.
3. If n(A)= a and n(B) = b then n(A B) = ab.
4. If A is empty or B is empty then A B is empty.
5. If one of the sets A and B is infinite the other is non-empty then A B is also infinite.

Example:
If A = {1,3,5} and B = {2,4}, then find A B and B A and also find n(A B).
Solution:
(i). A B = {1,3,5} {2,4}
= {(1,2),(1,4),(3,2),(3,4),(5,2),(5,4)}

(ii). B A = {2,4} {1,3,5}
= {(2,1),(2,3),(2,5),(4,1),(4,3),(4,5)}

(iii). n(A B) = n(A) * n(B)
Where n(A) and n(B) are the number of elements in the set A and B respectively.
n(A B) = 3 * 2
= 6


Directions: Choose the correct answer. Also write at least 5 examples of your own.
Q 1: If A = {1,2,3} and B = {4,5} then find B A.
{(1,4),(1,2),(2,4),(2,5),(3,4),(3,5)}
{(1,4),(1,5),(2,3),(2,5),(3,4),(3,5)}
{(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)}
{(1,3),(1,5),(2,4),(2,3),(3,4),(3,5)}

Q 2: If A = {1,2,3} and B = {3,4} then find A B.
{(1,3),(1,4),(2,3),(2,4),(3,1),(3,4)}
{(1,3),(1,5),(2,3),(2,4),(3,3),(3,4)}
{(1,3),(1,4),(3,2),(2,4),(3,3),(3,4)}
{(1,3),(1,4),(2,3),(2,4),(3,3),(3,4)}

Q 3: If A = {1,2,3,4} and B = {6,7} then find A B.
{(1,6),(1,8),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7)}
{(1,5),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7)}
{(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,5)}
{(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7)}

Q 4: If A = {1,2,3,4,5,6} and B = {2,3,4,5} then find n(A B).
26
25
24
28

Q 5: If A = {2,3,4} and B = {5,6} then find A B.
{(2,5),(2,6),(3,5),(3,6),(4,2),(4,6)}
{(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)}
{(2,5),(2,4),(3,5),(3,6),(4,5),(4,6)}
{(2,5),(2,6),(3,6),(3,6),(4,5),(4,6)}

Q 6: If A = {2,4,6} and B = {1,3} then find B A.
{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6)}
{(1,2),(1,4),(1,6),(3,1),(3,4),(3,6)}
{(1,2),(1,4),(1,6),(3,2),(3,1),(3,6)}
{(1,3),(1,4),(1,6),(3,2),(3,4),(3,6)}

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Question 8: This question is available to subscribers only!


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