Question:
A and B are any two non-empty sets and A is proper subset of B. If n(A) = 5, then the minimum possible value of n(A ∆ B) is___________.
Solution:
Given A ∩ B = ϕ
$A \subseteq B$ and $n(A)=5$
Then minimum possible value of n(A ∆ B)
Since $A \subsetneq B \quad$ i.e $n(A) \subsetneq n(B)$
⇒ A ⋃ B = B
A ∩ B =
n(A ∆ B) = n(A ⋃ B) – n(A ∩ B)
= n(B) – n(A)
= n(B) – 5
i.e n(A ∆ B) = – n(B) – 5 > n(A) – 5 = 0
i.e. n(A ∆ B) > 0
Minimum possible value of n(A ∆ B) = 1
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