Question

Let A be the set of 20 even numbers and B be the set of 22 multiples of 3. then the maximum number of elements in A U B?

Answer 1

Given,

Let A be the set of 20 even numbers.

Let B be the set of 22 multiples of 3.

To find,

The maximum number of elements in AUB.

Solution,

We denote number of elements in a set as n ( set).

Let the number of elements in set AUB = n (AUB).

Let the number of elements in set A = n (A).

Let the number of elements in set B = n (B).

Let the number of elements in set A∩B = n (A∩B).

We know, according to set theory the number of elements in AUB is given by the formula = n (AUB) = n (A )+ n (B) - n (A∩B)

Now, the number of elements to be maximum in AUB, the negative term that is A∩B has to be minimum which is equal to 0.

Here, n (A) = 20 and n (B) = 22.

Therefore,

⇒ n (AUB) = n (A )+ n (B) - n (A∩B)

⇒ n (AUB) = n (A )+ n (B) - 0

⇒ n (AUB) = n (A )+ n (B)

⇒ n (AUB) = 20 + 22

⇒ n (AUB) = 42

Hence, the maximum number of elements in AUB is 42.