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}.
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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.
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