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4. (a) If A and B are two disjoint sets and n(A) = 30, n(B) = 40, find n(AUB). (b) If A and B are disjoint sets and n(AUB) = 40, n(A) = 25, find n(B). 5. (a) From the given diagram find the​



Answer :

rvkacademic

Answer:

n(A U B) = 70

n(B) = 15

Step-by-step explanation:

First let's understand what disjoint sets are

Here is the official clang on this

Disjoint Sets
In set theory in mathematics and formal logic, two sets are said to be disjoint sets if they have no element in common (Wikipedia)

Say you have
A = {1, 2, 3}
B= {4, 5, 6, 7}

A and B are disjoint sets since they have no element in common

The cardinality of a set is defined as the number of elements in that set

Therefore in the above toy example,
n(A) = 3
n(B) = 4

n(A ∪ B)= number of elements in set A or set B and for disjoint sets that is simply the sum of the number of elements in each set:

With
n(A) = 30
n(B) = 40

n(A U B) = 30 + 40 = 70

By the same reasoning if
n(A U B) = 40 then
n(B) = n(A U B) - n(A) = 40 - 25 = 15

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