15. If A={1,3,4,5,6} & B={2,5,6,7}, then n(A∩B)= *
{5,6}
{2}
(5,6)
2
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Answers
Given :- A = {1,3,4,5,6} & B = {2,5,6,7} .
To Find :- n(A∩B) =
A) {5,6}
B) {2}
C) (5,6)
D) 2 .
Solution :-
we know that,
- n means the number of elements in the set . when A = {1,2,3,4,5} , n(A) = 5 .
given that,
→ A = {1, 3, 4, 5, 6}
→ B = {2, 5, 6, 7}
so,
→ n(A) = 5 elements.
→ n(B) = 4 elements.
then,
→ (A∩B) = common elements between set A and set B = {5, 6}
therefore,
→ n(A∩B) = 2 elements .
Hence , option (D) 2 is correct answer .
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SOLUTION
TO CHOOSE THE CORRECT OPTION
If A = { 1,3,4,5,6 } & B = { 2,5,6,7 } ,
then n( A ∩ B ) =
- {5,6}
- {2}
- (5,6)
- 2
CONCEPT TO BE IMPLEMENTED
SET :
A set is a well defined collection of distinct objects of our perception or of our thought to be conceived as a whole
Representation of Set :
A set can be represented in following ways
(i) Statement form method
(ii) Roster or tabular form method
(iii) Rule or set builder form method
EVALUATION
We know that for two given sets A and B , the intersection of the sets A and B is denoted by A ∩ B and defined as
A ∩ B = { x : x ∈ A ∧ x ∈ B }
More precisely A ∩ B is set of all elements which are in both the sets A and B
Now it is given that
A = { 1,3,4,5,6 }
B = { 2,5,6,7 }
We see that the elements 5 and 6 are in both A and B
So A ∩ B = { 5 , 6 }
Thus we have
n( A ∩ B )
= The number of elements in A ∩ B
= 2
Venn Diagram : Venn diagram is referred to the attachment
In the Venn diagram we see that the number of elements in A ∩ B is 2
FINAL ANSWER
Hence the correct option is 2
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