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Operations on sets Class 8 Math Worksheet – 30 Marks
[Operations on sets]
1) Write the power set of the following sets. [1 × 2] = 2
(i) {-1, -1}
(ii) {x, y, z}
(2) Verify: [1 × 4] = 4
(a) X ∪ Y = Y ∪ X
(b) X ∩ Y = Y ∩ X, when
(i) X = {1, 2, 3, ……10}, Y = {7, 8, 9, 10, 11, 12}
(ii) X = {1, 2, 3, ……15}, Y = {6, 8, 10, ……, 20}
(3) Show that: [1 × 2] = 2
if X = {a, b, c}, Y = {b, d, f} and Z = {a, f, c}
X ∪ (Y ∩ Z) = (X ∪ Y} ∩(X ∪ Z)
(4) Verify De Morgan’s Laws if: [1 × 2] = 2
U = N, A = φ, and B = P
(5) Write all subsets of the following sets. [1 × 2] = 2
(i) { }
(ii) {1}
(iii) {m, n}
(6) Verify the commutative law of union and intersection of the following sets through Venn diagrams. [1 × 4] = 4
(i) P = {3, 5, 7, 9, 11, 13}
Q = {5, 9, 13, 17, 21, 25}
(ii) The sets N and Z
(iii) R = {x|x ∈ N ^ 8≤ x ≤18}
S = {y|y ∈ N ^ 9≤ y ≤19}
(iv) The sets is and O
(7) Write all subsets of the following sets. [1 × 3] = 3
(i) X = {e ,f, g} and Y = {1,3,5}
(ii) Write the power set of {a, b, c}
(iii) Verify De Morgan’s Laws if U = {a, b, c, d, e}, X = {9, 6} and Y = {a,b,c}
(8) For the given sets, verify the following laws through venn diagram. [1 × 4] = 4
(i) Associative law of Union of sets.
(ii) Associative law of Intersection of sets.
(iii) Distributive law of Union over intersection of sets.
(iv) Distributive law of Intersection over Union of sets.
(a) X = {2,4, 6,8,10,12}, Y = {1,3,5,7,9,11} and Z = {3, 6,9,12,15}
(b) X = {x|x ∈ Z^8≤ x ≤25}, Y = {y|y ∈ Z^ – 2< y <6} and Z = {z|z ∈ z ^ z78}
(9) Write the short answers of the following questions. [1 × 4] = 4
(i) Define a set.
(ii) What is the difference between whole numbers and natural numbers?
(iii) Define the proper and improper subsets.
(iv) Define a power set. v. Define De Morgan’s Laws.
(10) Write all proper subsets of the following sets. [1 × 3] = 3
(i) {a}
(ii) {0, 1}
(iii) {1 , 2, 3}