Q1. From the given sets, identify the disjoint sets:
(i) {1, 2, 3, 4} and {x: x is a natural number and 4 ≤ x ≤ 6}
(ii) {a, e, I, o, u} and {c, d, e, f}
(iii) {x: x is an even integer} and {x: x is an odd integer}
Q2. Find the union of the following sets:
A = {x: x is an even integer} and B = {x: x is an odd integer}
Q3. Find the intersection of the following pair of sets:
(i) A = (x: x is a natural number and multiple of 2}
B = {x: x is a natural number less than 6}
(ii)
X = {set of prime number}
Q4. Show that
Y = {set of odd natural numbers}
, {0} and 0 are all different.
Q5. State the cardinal number of the following sets:
(i) A = {set of letters in the word ‘COMMON’}
(ii) B = {Triangles with four sides}
(iii)
C = {x/x
N, x lies between 5 and 9}
Q6. Verify for equal sets: Give reason for your answer.
A = {2, 4, 6, 8} and B = {2n: n
N and n < 5}
Q7. Classify the following as disjoint or overlapping sets:
(i) {flowers in a garden} and {butterflies in a garden}
(ii)
{set of square numbers less than 17} and {set of multiples of 3}
(iii)
{a, b, c} and {p, q, r}
Q8. Identify the following sets as finite or infinite:
(i) Set of all triangles in a plane.
(ii) A = {x: x is a student of class VI}
(iii) Set of all counting numbers
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(iv)
C = {x: x
W, x < 4}
Q9. List the elements of the following sets then find A
A = {x: x
N, x ≤ 4} and B = {x
B and A
B.
W: 2 ≤ x ≤ 6}
Q10. If A = {0, 1, 2, 3, 4, 5}; B = {0, 2, 4, 6, 8} and C = {0, 3, 6, 9} then show that:
A
(B
C) = (A
B)
C.
Q11. State, if the given sets are equivalent or not, give reason.
(i)
A = {5, 6, 7} and B = {x: x
W and x ≤ 4}
(ii)
Set of whole numbers and set of multiples of 3
Q12. Write True or False for the following statements:
(i)If set A = set B then n(A) = n(B)
(ii)
If A = {factors of 16} and B = {factors of 20}, then A = B
(iii)
If A = {x; x is an even prime number}, then set A is empty.
(iv)
If A = {x: x is a perfect square and P ≤64}, then n(A) = 64
Q13. If A = x: x is a natural number}, B = {x: x is an even natural number},
C = {x: x is an odd natural number} and D = {x: x is a prime number}, find
(i) A
B (ii) A
C
Q14. List the members of the following sets:
(i)
{7, 8, 9, 10}
{11, 12, 13, 14}
(ii)
{dog, fish, cow}
{horse, rabbit, cow}
Q15. Fill in the blanks to make each statement a true statament:
(i) A
A = … (ii)
A=…
Q16.What are equal sets? In the following, state whether A = B or not:
(i) A = {4, 5, 6 7} B ={7,4,5,6}
(ii) A = {cat, dolphin, octopus, gold fish} B = {Tiger, lion, Jackal, Horse}
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Q17. Are the following sets are equal? Justify your answer.
X, is a set of letters in ‘ALLOY’ and B, is a set of letters in ‘LOYAL’
Q18. If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find
(i) B
D
(ii) A
C
Q19. If A = x: x is a natural number}, B = {x: x is an even natural number},
C = {x: x is an odd natural number} and D = {x: x is a prime number}, find
(i) A
D
(ii) B
C
Q20. Find the union of the following sets:
(i)
A = {1, 2, 3}, B =
(ii) B = {3, 4, 5, 6}, C = {5, 6, 7, 8}, D = {7, 8, 9, 10}
Find B
C
D
ANSWERS:
A1. Pair of (iii) is disjoint sets.
A2. (i) A
B = {x: x is an even or odd integer}
A3. (i) A
B = {3}
(ii) X
A4.
Y = {3, 5, 7, 11,13….}
is a set containing no elements at all.
{0} is a set containing one element, hence it is a singleton set.
0 is a number and not a set.
A5. (i) 4
(ii) 0
(iii) 3
A6. Hint: List the elements of set B.
A = B since the two sets have exactly the same elements.
A7. (i) Disjoint sets
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(ii) overlapping sets
(iii) overlapping sets
A8. (i) Infinite (ii) Finite
(iii) Infinite (iv) finite
A9. A = {1, 2, 3, 4} and B = {2, 3, 4, 5, 6}
A
B = {1, 2, 3, 4, 5, 6} and A
A10.Hint: (i) Find (B
Similarly find (A
C) then A
B)
B = {2, 3, 4}
(B
C) = {0, 1, 2, 3, 4, 5, 6, 8, 9}
C.
A11. (i) Not equivalent as the two sets do not contain the same number of elements.
(i)
Equivalent; as both the sets have infinite number of elements.
A12. (i) True
(ii) False
(iii) False
A13. (i) A
(iv) false
B = B (ii) A
C=C
A14. (i) {7,8,9,10,11,12,13, 14}
A15. (i) A
A = A (ii)
(ii){dog, fish, cow, horse, rabbit}}
A=A
A16. Two sets are said to be equal when they have exactly the same elements.
(i) Equal sets (ii) not equal sets.
A17. X and B are equal sets.
X = {A, L, L, O, Y} and B = {L, O, Y, A, L} Repetition of elements in a set do not
change a set.
A18. (i) (i) B
A19. (i) A
A20. (i) A
(ii) B
D=
D=D
(ii) A
(ii) B
C = {11}
C=
B = {1, 2, 3}
C
D = {3, 4, 5, 6, 7, 8, 9, 10}
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