let A and B be two sets aside a has 2016 more subsets then b a intersection b has three members then number of members of a union b is
Answers
Given : A and B two sets , a has 2016 more subsets then b . a intersection b has three members
To find : number of members of a union b n(A U B)
Solution:
Let say A Has a element
& B Has b elements
A has 2016 more subsets than B
2ᵃ - 2ᵇ = 2016
=> 2ᵃ - 2ᵇ = 32 * 63
=> 2ᵃ - 2ᵇ = 2⁵ * (2⁶ - 1)
=> 2ᵇ(2ᵃ⁻ᵇ - 1) = 2⁵ * (2⁶ - 1)
=> b = 5 , a-b = 6
=> a = 11
n(A) = 11
n(B) = 5
n(A ∩ B) = 3
n(A U B) = n(A) + n(B) - n(A ∩ B)
=> n(A U B) = 11 + 5 - 3
=> n(A U B) = 13
number of members of a union b is 13
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