Class 11 Maths NCERT Solutions Chapter 1 Ex 1.2 – Empty, Finite, Infinite and Equal Sets

An odd number is never divisible by 2.

So no natural number can satisfy both conditions.

2 is even, and 2 is prime.

So the set = {2}.

No natural number can be less than 5 and greater than 7 at the same time.

Parallel lines never intersect, so they have no point in common.

There are exactly 12 months in a year.

Natural numbers do not end at any last element.

This set has exactly 100 elements, from 1 to 100.

101, 102, 103, ... continue without end.

The primes less than 99 are 2, 3, 5, 7, ..., 97 — a definite, countable list.

For every real number c, the line y = c is parallel to the x-axis.

There are infinitely many real numbers c.

There are exactly 26 letters.

5, 10, 15, 20, ... continue without end.

However large, the number of animals alive at any time is a definite number.

A circle through the origin can be drawn with any centre, taking the radius equal to the distance of that centre from the origin.

There are infinitely many such centres.

Both sets contain exactly a, b, c, d.

Order of elements does not matter in a set.

12 ∈ A but 12 ∉ B.

18 ∈ B but 18 ∉ A.

The positive even integers up to 10 are 2, 4, 6, 8, 10.

So B = {2, 4, 6, 8, 10}, the same elements as A.

A = {10, 20, 30, 40, ...}, containing only multiples of 10.

15 ∈ B, but 15 is not a multiple of 10, so 15 ∉ A.

x^2+5x+6=0

\Rightarrow (x+2)(x+3)=0

\Rightarrow x=-2 \text{ or } x=-3

So B = {−2, −3}.

Listing distinct letters only (repetition does not create a new element):

A = {F, O, L, W}

B = {W, O, L, F}

Both sets contain exactly the same four letters.

B = {1, 2, 3, 4} and D = {3, 1, 4, 2} contain exactly the same elements.

E = {−1, 1} and G = {1, −1} contain exactly the same elements.

A = {2, 4, 8, 12} and C = {4, 8, 12, 14}: 2 ∈ A but 2 ∉ C, and 14 ∈ C but 14 ∉ A.

F = {0, a} and H = {0, 1}: these match only if a = 1, which is not given.