ClassesClass 10MathematicsSetsExercise 1.5

Sets

Exercise 1.5

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Exercise 1.5 All Exercises

Problems

7 total

Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = { 1, 2, 3, 4}, B = { 2, 4, 6, 8 } and C = { 3, 4, 5, 6 }. Find (i) A' (ii) B' (iii) (A \cup C)' (iv) (A \cup B)' (v) (A')' (vi) (B - C)'

If U = { a, b, c, d, e, f, g, h }, find the complements of the following sets : (i) A = {a, b, c} (ii) B = {d, e, f, g } (iii) C = {a, c, e, g} (iv) D = { f, g, h, a}

Taking the set of natural numbers as the universal set, write down the complements of the following sets: (i) {x : x is an even natural number} (ii) { x : x is an odd natural number } (iii) {x : x is a positive multiple of 3} (iv) { x : x is a prime number } (v) {x : x is a natural number divisible by 3 and 5} (vi) { x : x is a perfect square } (vii) { x : x is a perfect cube} (viii) { x : x + 5 = 8 } (ix) { x : 2x + 5 = 9} (x) { x : x \geq 7 } (xi) { x : x \in N and 2x + 1 > 10 }

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that (i) (A \cup B)' = A' \cap B' (ii) (A \cap B)' = A' \cup B'

Draw appropriate Venn diagram for each of the following : (i) (A \cup B)', (ii) A' \cap B', (iii) (A \cap B)', (iv) A' \cup B'

Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A'?

Fill in the blanks to make each of the following a true statement : (i) A \cup A' = . . . (ii) φ' \cap A = . . . (iii) A \cap A' = . . . (iv) U' \cap A = . . .