Class 11 Maths NCERT Solutions Chapter 1 Sets

Representation of Sets and its elements is done as follows: 

• Roster Form: In this form, all elements are enclosed within braces {} and they are separated by commas (,). For example, a collection of all the numbers found on a dice N = {1, 2, 3, 4, 5, 6}. 
• Set Builder Form: In this form, all elements hold a common property which is not featured by any other element outside the Set. For example, a group of vowels in English alphabetical series.

Example: Determine if the given set is an empty set. P = {set of prime numbers divisible by 6}.

Solution: Given: P = {set of prime numbers divisible by 6}

As per the definition of prime numbers, prime numbers are the numbers that have only two factors, that are, 1 and the number itself.

Therefore, no prime numbers are divisible by 6.

This implies that the given set is an empty set.

Example 3: Given, Set T = {….., -2, -1, 0}. Find out whether the given set is a finite or infinite set.

Solution: Set T = {….., -2, -1, 0} is an infinite set because the elements of the set T start from negative of infinity and hence, cannot be finite.

Example: Check if the sets A = {a, e, i, o, u} and B = {e, i, a, o, u} are equal sets or unequal sets.

Solution: The order of the elements does not impact the equality of the two sets.

Thus, set B can be written as B = {a, e, i, o, u} after rearranging the elements of B.

Hence, A = {a, e, i, o, u} = B

Thus, Sets A and B are equal sets.

A ⊆ B