Mathematics
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}.
Sets
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Answer
(i)
A = {x : x is a prime number, x < 8}.
B = {x : x is an even natural number, x < 8}.
Roster Form of A = {2, 3, 5, 7}
Roster Form of B = {2, 4, 6}
Both sets share the element {2}.
∴ These are overlapping sets
(ii) C = {x : x ∈ N, x < 10} and D = {x : x ∈ N, x is a multiple of 5}.
Roster Form of C = {1, 2, 3, 4, 5, 6, 7, 8, 9}
Roster Form of D = {5, 10, 15, 20, }
The number 5 is present in both sets.
∴ These are overlapping sets
(iii) E = {x : x = 4n, n ∈ N} and F = {x : x = 9n, n ∈ N}.
Roster Form of E = {4, 8, 12, 16, 20, 24, 28, 32, 36, ….}
Roster Form of F = {9, 18, 27, 36, 45, ….}
The first common multiple is 36. Since these are infinite sets of multiples, they will continue to have common elements (like 72, 108, etc.).
∴ These are overlapping sets
(iv) G = {x : x = 8n, n ∈ N and n < 7} and H = {x : x = 9n, n ∈ N and n < 7}.
Roster Form of G = {8, 16, 24, 32, 40, 48} (Multiples of 8 up to n=6)
Roster Form of H = {9, 18, 27, 36, 45, 54} (Multiples of 9 up to n=6)
There are no common elements in these finite lists. The first shared multiple of 8 and 9 is 72, which is outside the range of both sets.
∴ These are disjoint sets
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Related Questions
Identify the null sets among the following :
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(iii) C = {x : x is an even prime number}.
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(v) E = {x : x is a perfect square number, 40 < x < 50}.
(vi) F = {x : x ∈ N, 5 < x < 6}.
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}.
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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}.
State in each case, whether the given statement is true or false :
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(iii) If C is the set of all prime numbers less than 80, then 57 ∈ C.
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(viii) 0 ∈ Φ.
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Indicate whether the given statement is true or false :
(i) {Triangles} ⊆ {Quadrilaterals}
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(iii) {Rhombuses} ⊆ {Parallelograms}
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(v) {Integers} ⊆ {Whole numbers}
(vi) {Composite numbers} ⊆ {Odd numbers}