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InterviewSolution
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Which of the following are examples of the singleton set? (i) {x : x ϵ Z, x2 = 4}. (ii) {x : x ϵ Z, x + 5 = 0}. (iii) {x : x ϵ Z, |x| = 1}. (iv) {x : x ϵ N, x2 = 16}. (v) {x : x is an even prime number} |
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Answer» (i) Integers = …-3, -2, -1, 0, 1, 2, 3, … Given equation: x2 = 4 ⇒ x = √4 ⇒ x = ± 2 If x = -2, then x2 = (-2)2 = 4 If x = 2, then x2 = (2)2 = 4 So, there are two elements in a set. ∴ It is not a singleton set. (ii) Integers = -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, … Given equations: x + 5 = 0 ⇒ x + 5 – 5 = 0 – 5 ⇒ x = -5 So, there is only 1 element in a given set. ∴ It is a singleton set. (iii) Integers = …, -2, -1, 0, 1, 2, … Given equation: |x| = 1 If x = -1, then |x| = |-1| = 1 If x = 1, then |x| = |1| = 1 So, there are 2 elements in a given set ∴ It is not a singleton set. (iv) Natural Numbers = 1, 2, 3, … Given equation: x 2 = 16 ⇒ x = √16 ⇒ x = ± 4 ⇒ x = -4, 4 but x = -4 not possible because x ∈ N So, there is only 1 element in a set. ∴ It is a singleton set. (v) Prime number = 2, 3, 5, 7, 11, … Even Prime number = 2 ∴ It is a singleton set. |
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