|Class 11 Maths Sets||Number of Elements in a set|
Number of Elements in a set
If A, B and C are finite sets, then
Explanation for n ( A ∪ B ) = n ( A ) + n ( B ) – n ( A ∩ B ): Since the common elements A ∩ B is counted twice with both n ( A ) & n ( B ) , we subtract it.
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Numerical: In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and mathematics. How many teach physics ?
Solution: Let P denote Physics teachers & M denote Maths Teacher.
n(M) = 12
n(M ∪ P) = 20
n(M ∩ P) = 4
Applying formula n ( M ∪ P ) = n ( M ) + n (P ) – n ( M ∩ P )
Or 20 = 12 + n(P) – 4
Or n(P) = 12
We can also solve this with Venn diagram
Numerical: A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports ?
We can represent the data using Venn diagram.
Or 58 =(35-a-b) + a + (12-a-c) + 3 + b + (17-b-c) + c
Or a+b+c =9
Thus 9 people received 2 medals.
Thus we can say that 3 men received 3 medals, 9 men received 2 medals & 26 men received 1 medal.
For good explanation of these concepts, refer ExamFear video lessons.