Mathematics
Identify the null sets among the following :
(i) A = {x : x is a whole number, x < 1}.
(ii) B = {x : x is a number, x > x}.
(iii) C = {x : x is an even prime number}.
(iv) D = {x : x ∈ I, x2 = -4}.
(v) E = {x : x is a perfect square number, 40 < x < 50}.
(vi) F = {x : x ∈ N, 5 < x < 6}.
Answer
(i) A = {x : x is a whole number, x < 1}.
Whole numbers start from 0. The only whole number less than 1 is 0.
A = {0}, it contains one element.
∴ It is not a null set.
(ii) B = {x : x is a number, x > x}.
Mathematically, no number can be strictly greater than itself.
∴ It is a null set.
(iii) C = {x : x is an even prime number}.
The number 2 is the only even prime number.
C = {2}
∴ It is not a null set.
(iv) D = {x : x ∈ I, x2 = -4}.
The square of any integer (I) is always non-negative (e.g., 22 = 4 and (-2)2 = 4). There is no integer whose square is -4.
D = { }
∴ It is a null set.
(v) E = {x : x is a perfect square number, 40 < x < 50}.
Perfect squares near this range are 62 = 36 and 72 = 49. Since 49 falls between 40 and 50, the set contains an element.
E = {49}
∴ It is not a null set.
(vi) F = {x : x ∈ N, 5 < x < 6}.
Natural numbers (N) are counting numbers (1, 2, 3, …..). There is no natural number between 5 and 6.
F = { }
∴ It is a null set.
Related Questions
State whether the given set is finite or infinite :
(i) Set of all even natural numbers.
(ii) Set of all odd integers.
(iii) Set of all rivers in India.
(iv) Set of all points on a line segment 1 cm long.
(v) Set of all factors of 1200.
(vi) Set of all multiples of 6.
(vii) Set of all drops of water in a bucket.
Identify whether the given pair consists of equal or equivalent but not equal sets or none :
(i) A = set of letters of the word 'FLOWER'.
B = set of letters of the word 'FOLLOWER'.(ii) C = {x : x ∈ N, x + 5 = 6} and D = {x : x ∈ W, x < 1}.
(iii) E = set of first five whole numbers.
F = set of first five natural numbers.(iv) G = {a, b, c} and H = {x, y, z}.
(v) J = {x : x ∈ N, x ≠ x} and K = {x : x ∈ N, 6 < x < 7}.
For each of the following pairs of sets, identify the disjoint and overlapping sets :
(i)
A = {x : x is a prime number, x < 8}.
B = {x : x is an even natural number, x < 8}.(ii) C = {x : x ∈ N, x < 10} and D = {x : x ∈ N, x is a multiple of 5}.
(iii) E = {x : x = 4n, n ∈ N} and F = {x : x = 9n, n ∈ N}.
(iv) G = {x : x = 8n, n ∈ N and n < 7} and H = {x : x = 9n, n ∈ N and n < 7}.