Let U = {1, 2, 3, ...., 20}. Let A, B, C be the subsets of U. Let A be

1.	Let U = {1, 2, 3, ...., 20}. Let A, B, C be the subsets of U. Let A be the set of all numbers which are perfect squares, B be the set of all numbers which are multiples of 5 and C be the set of all numbers which are divisible by 2 and 3.Consider the following statements:1. A, B, C are mutually exclusive.2. A, B, C are mutually exhaustive.3. The number of elements in the complement set of A ∪ B is 12.Which of the statements given above the correct?1. 1 and 2 only2. 1 and 3 only3. 2 and 3 only4. 1, 2 and 3
Answer» Correct Answer - Option 2 : 1 and 3 only Concept: Let U be the universal set and A, B, C be the subsets of U. If \(\rm A∩ B ∩ C = \phi\) then A, B, C are mutually exclusive. Çalculations: Given, U = {1, 2, 3, ...., 20}. Let A, B, C be the subsets of U. A be the set of all numbers which are perfect squares ⇒ A = {1, 4, 9 16} B be the set of all numbers which are multiples of 5 ⇒ B = {5, 10, 15, 20} and C be the set of all numbers, which are divisible by 2 and 3 ⇒ C = {6, 12, 18} Now, \(\rm A∩ B ∩ C = \phi\) So, Å, B, C are mutually exclusive. Hence statement 1 is correct Here Å, B, C are mutually exclusive so A, B, C can't be mutually exhaustive Hence statement 2 is wrong A ∪ B = {1, 4, 5, 9, 10, 15, 16, 20} n(A ∪ B) = 8 U = {1, 2, 3, ...., 20} n(U) = 20 Now, The number of elements in the complement set of A ∪ B = n(U) - n(A ∪ B) = 20 - 8 = 12 Hence statement 3 is correct

Let U = {1, 2, 3, ...., 20}. Let A, B, C be the subsets of U. Let A be the set of all numbers which are perfect squares, B be the set of all numbers which are multiples of 5 and C be the set of all numbers which are divisible by 2 and 3.Consider the following statements:1. A, B, C are mutually exclusive.2. A, B, C are mutually exhaustive.3. The number of elements in the complement set of A ∪ B is 12.Which of the statements given above the correct?1. 1 and 2 only2. 1 and 3 only3. 2 and 3 only4. 1, 2 and 3

Answer» Correct Answer - Option 2 : 1 and 3 only

Concept:

Let U be the universal set and A, B, C be the subsets of U.

If \(\rm A∩ B ∩ C = \phi\) then A, B, C are mutually exclusive.

Çalculations:

Given, U = {1, 2, 3, ...., 20}.

Let A, B, C be the subsets of U.

A be the set of all numbers which are perfect squares

⇒ A = {1, 4, 9 16}

B be the set of all numbers which are multiples of 5

⇒ B = {5, 10, 15, 20}

and C be the set of all numbers, which are divisible by 2 and 3

⇒ C = {6, 12, 18}

Now, \(\rm A∩ B ∩ C = \phi\)

So, Å, B, C are mutually exclusive.

Hence statement 1 is correct

Here Å, B, C are mutually exclusive so A, B, C can't be mutually exhaustive

Hence statement 2 is wrong

A ∪ B = {1, 4, 5, 9, 10, 15, 16, 20}

n(A ∪ B) = 8

U = {1, 2, 3, ...., 20}

n(U) = 20

Now, The number of elements in the complement set of A ∪ B = n(U) - n(A ∪ B) = 20 - 8 = 12

Hence statement 3 is correct