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Exercise 7 - Example(Page 1) 		Home
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Children are standing in the line as follows:
  Column 1 Column 2 Column 3
Row 1 James Clara Sid
Row 2 Sam Mat Jen
Row 3 Nat Amanda Anna
Ordered pair for James is (1,1). Ordered pair for Clara is (1,2). Ordered pair for Sid is (1,3).
Ordered pair for Sam is (2,1). Ordered pair for Mat is (2,2). Ordered pair for Jen is (2,3).
Ordered pair for Nat is (3,1). Ordered pair for Amanda is (3,2). Ordered pair for Anna is (3,3).

If ordered pair is given, we can find the person who is standing at that place.

Ordered pair: An ordered pair is a pair of elements, written in a specific order. The first element taken from first set and the second element taken from second set.


Example 1: A = {1,2,3} B = {8,9}

A x B = {(1,8), (1,9), (2,8), (2,9), (3,8), (3,9)}

B x A = {(8,1), (8,2), (8,3), (9,1), (9,2), (9,3)}

A x B B x A

n(A x B) = n(A) x n(B) = 3 x 2 = 6
n(B x A) = n(B) x n(A) = 2 x 3 = 6
Cross Product or Cartesian Product of two sets: Cross Product or Cartesian Product of set A and B is the set of all possible ordered pairs and is denoted by A x B
n(A x B) = n(A) x n(B)


Tree Diagram for A x B

A x B = {(1,8), (1,9), (2,8), (2,9), (3,8), (3,9)}



Arrow Diagram for A x B

A x B = {(1,8), (1,9), (2,8), (2,9), (3,8), (3,9)}



Arrow Diagram for B x A

B x A = {(8,1), (8,2), (8,3), (9,1), (9,2), (9,3)}


Example 2:
A = {2,4}, B = {1,3}, C = {1,2,3}.
Find:(A B) x (B C) and n[(A B) x (B C)]
(A B) = {1,2,3,4)
(B C) = {1,3}
(A B) x (B C) = {(1,1), (1,3), (2,1), (2,3), (3,1), (3,3), (4,1), (4,3)}
n[(A B) x (B C)] = 8

Power set: The set containing all the subsets of a given set is called power set. The power set of set B is denoted by P(B).
Example 3:
Let B = {2,4,6}
P(B) = [{ }, {2}, {4}, {6}, {2,4}, {4,6}, {2,6}, {2,4,6}]

Cardinal number of Power set: It is equal to the number of subsets formed from the given set and
denoted by n[P(B)]. If there are "n" elements in set B then n[P(B)] = 2n
Example 4:
Let B = {2,4,6}
P(B) = [{ }, {2}, {4}, {6}, {2,4}, {4,6}, {2,6}, {2,4,6}]
n[P(B)] = 8 = 23

Example 5:
Let n[P(B)] = 8, find n(B).
n[P(B)] = 8 = 23
n(B) = 3

Example 6:
Let n[P(B)] = 32, find n(B).
n[P(B)] = 32 = 25
n(B) = 5


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