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Question

Let S={1,2,3,,n} and A={(a,b)|1a,bn}=S×S. A subset B of A is said to be a good subset if (x,x)B for every xS. Then the number of good subsets of A is

A
1
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B
2n
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C
2n(n1)
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D
2n2
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Solution

The correct option is B 2n(n1)
Number of elements in B =n×n=n2
No of elements of type (x,y) =n2n
After choosing n elements
We can choose any number of elements from n2n elements
Number of subsets =Cn2n0+Cn2n1+Cn2n2...........Cn2nn2n
As Cn0+Cn1+Cn2.....Cnn=2n
Cn2n0+Cn2n1+Cn2n2...........Cn2nn2n=2n2n
So option C is correct


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