Question

X={1,2,3,.......,10} and A ={1,2,3,4,5}, find the number of subsets of B if B is the subset of X such that A-B ={4}​
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Answer 1

Given :-

◉ X = {1,2,3,...,10} , A= {1,2,3,4,5}

◉ a set B which is the subset of X such that A - B = { 5 }

To Find :-

◉ Number of subsets of B

Answer :-

To find the number of elements of a set, at first we should know the number of elements because number of subsets = 2ⁿ where, n is the number of elements.

⇒ A = {1,2,3,4,5}

And, A - B = {4}

⇒ A - B = Elements in A and not in B

From the above statement,

⇒ B = {1,2,3,5} ⊂ X

Now, That we know the number of elements in B which is 4.

∴ Number of Subsets = 2⁴ = 16

Some Information :-

⇒ A U B = { x : x ∈ A or x ∈ B }

⇒ A ⋂ B = { x : x ∈ A and x ∈ B }

⇒ Number of subsets of a set A which has n elements is 2ⁿ