Question

Let A={1,2,3), B={2,3,4}, C={1,3,5),
D={2,3}. Find the cardinality of sum
of all the sets.

Options Are:

a- 6
b- 7
c- 5
d- 4​

Answer 1

The cardinality of sum of all the sets = 5

Given :

A = { 1 , 2 , 3 } , B = { 2 , 3 , 4 } , C = { 1 , 3 , 5 } , D = { 2 , 3 }.

To find :

The cardinality of sum of all the sets is

a. 6

b. 7

c. 5

d. 4

Solution :

Step 1 of 3 :

Define Union of sets

For two given sets M and N , the union of the sets is denoted by M ∪ N and defined as

M ∪ N = { x : x ∈ M ∨ x ∈ N }

Step 2 of 3 :

Find sum of all the sets

Here the given sets are

A = { 1 , 2 , 3 } , B = { 2 , 3 , 4 } , C = { 1 , 3 , 5 } , D = { 2 , 3 }.

So the sum of all the sets

= A ∪ B ∪ C ∪ D

= { 1 , 2 , 3 , 4 , 5 }

Step 3 of 3 :

Find cardinality of sum of all the sets

We know that cardinality of a set is defined as the total number of elements in the set

Since the total number of elements in the sum of all the sets are 5

So cardinality of sum of all the sets is 5

Hence the correct option is c. 5

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