1. Which of the
following is correct?
(1) {7} ∈ {1,2,3,4,5,6,7,8,9,10} (2)
7 ∈ {1,2,3,4,5,6,7,8,9,10}
(3) 7 ∉ {1,2,3,4,5,6,7,8,9,10} (4)
{7} Ë {1,2,3,4,5,6,7,8,9,10}
Answer:
(2) 7 ∈ {1, 2,
3, 4, 5, 6, 7, 8, 9, 10}
First
option is Set, 7, which not an element, third option given is 7 not an element,
but 7 is an element of the given set, and, Fourth option given is, Set, 7 is
not a subset of the given set. But, 7 is
an element of the given set, then Set, 7 is a subset of the given set.
2. The set P = {x | x ∈ Z, –1< x < 1} is a
(1) Singleton set (2) Power set
(3) Null set (4) Subset
Answer:
(1) Singleton set
When
we write the set in Roster form, we get, Set, P = {0}. Hence, there are only one element in Set,
P. Therefore, it is a singleton set.
3. If U ={x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is
(1) {1, 6, 7, 8, 9} (2) {1, 2, 3, 4}
(3) {2, 3, 4, 5} (4) { }
Answer:
(3) {2, 3, 4, 5}
When
we write the given sets in Roster form, we get,
Set,
U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and, Set, A = {2, 3, 4, 5}
Now
A’ = {1, 6, 7, 8, 9}
Hence,
(A’)’ = {2, 3, 4, 5}.
4. If B⊆ A then n(A ∩ B) is
(1) n(A–B) (2) n(B)
(3) n(B – A) (4) n(A)
Answer:
(2) n(B)
We
know that, When B⊆
A, then A ∩ B = B.
5. If A = {x, y, z}
then the number of non- empty subsets of A is
(1) 8 (2)
5
(3) 6 (4)
7
Answer:
(4) 7
Total
number of subsets of a set = 2n = 23 = 8. But, there includes null set also. When we exclude null set from the number of
subset, we get, 7.
6. Which of the
following is correct?
(1) ∅ ⊆ {a, b} (2) ∅ ∈ {a, b}
(3) {a} ∈ {a, b} (4)
a ⊆ {a, b}
Answer:
Ø ⊆ {a, b}
Null
set is a subset of every set.
7. If A∪B = A∩B, then
(1) A≠B (2) A = B
(3) A ⊂ B (4)
B ⊂ A
Answer:
(2) A = B
8. If B – A is B, then
A∩B is
(1) A (2)
B
(3) U (4)
∅
Answer:
(4) Ø
Given
B – A = B, then we know that, A and B are disjoint sets.
9. From the adjacent
diagram n[P(AΔB)] is
(1) 8 (2) 16
(3) 32 (4) 64
Answer:
(3) 32
A
∆ B = { 60, 85, 75, 90, 70}, ⇒
n(A ∆ B) = 5, ⇒
n(P(A ∆ B)) = 25 = 32
10. If n(A) = 10 and n(B) = 15, then the minimum
and maximum number of elements in A ∩ B is
(1) 10,15 (2) 15,10
(3) 10,0 (4) 0,10
Answer:
(4) (0, 10)
If
the two sets A and B are disjoint, then, A ∩ B has no elements. In the given numbers, there should be maximum
of 10 elements in A ∩ B.
11. Let A = {∅} and B = P(A), then A∩B is
(1) { ∅, {∅} } (2) {∅}
(3) ∅ (4)
{0}
Answer:
(2) {Ø}
Given,
Set A = Null Set. Then Power Set P(A) =
{∅,
{∅}},
That is, Set, B = {∅,
{∅}}. Now A ∩ B = {Ø}.
12. In a class of 50 boys, 35 boys play Carrom and
20 boys play Chess then the number of boys play both games is
(1) 5 (2)
30
(3) 15 (4)
10.
Answer:
(1) 5
Here,
Let A be the boys play carrom and Set, B be the boys play Chess. Total Strength of the class is 50. That is n(A ∪ B) = 50. n(A) = 35 and n(B) = 20. We know that, (A ∪ B) = n(A) +
n(B) – n(A ∩ B) ⇒
50 = 35 + 20 – n(A ∩ B) ⇒
n(A ∩ B) = 5.
13. If U = {x : x Î N and x <10}, A =
{1,2, 3,5, 8} and
B = {2,5,6,7,9}, then n[(A È B)’] is
(1) 1 (2)
2
(3) 4 (4)
8
Answer:
(1) 1
Converting
the given sets, in Roster Form, We get, U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A =
{1, 2, 3, 5, 8}, and, B = {2, 5, 6, 7, 9}.
A
∪
B = {1, 2, 3, 5, 6, 7, 8, 9}.
Now,
(A ∪
B)’ = {4},
n(A
∪
B)’ = 1
14. For any three sets P,
Q and R, P −(Q ∩ R) is
(1) P −(Q È R) (2) (P Ç Q)−R
(3) (P −Q) È (P −R) (4) (P −Q) Ç (P −R)
Answer:
(3) (P – Q) ∪
(P – R)
We
know that, P −(Q ∩ R) = (P – Q) ∪ (P – R)
15. Which of the
following is true?
(1) A−B = A Ç B (2) A−B = B −A
(3) (A È B)’ = A’ È B’ (4) (A Ç B)’ = A’ È B’
Answer:
(4) (A ∩ B)’ = A’ ∪ B’
16. If n(A È BÈ C) = 100, n(A) = 4x,
n(B) = 6x, n(C) = 5x, n(A Ç B) = 20, n(B Ç C) = 15, n(A Ç C) = 25 and n(A Ç B Ç C) = 10 , then the value of x is
(1) 10 (2)
15
(3) 25 (4)
30
Answer:
(1) 10
We
know that, n(A ∪
B ∪
C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(C ∩ A) + n(A ∩ B ∩ C)
Substituting
the values, we get,
100
= 4x + 6x + 5x – 20 – 15 – 25 + 10
100
= 15x -60 + 10
100
= 15x – 50
∴ 15x = 100 + 50
= 150
x
= 10
17. For any three sets A,
B and C, (A−B) Ç (B −C) is equal to
(1) A only (2) B only
(3) C only (4) Æ
Answer:
(4) ϕ
As
per the derivation, (A−B) Ç
(B −C) = Null Set.
18. If J = Set of three
sided shapes, K = Set of shapes with two equal sides and L = Set of shapes with
right angle, then J Ç K Ç L is
(1) Set of isosceles
triangles (2) Set of equilateral triangles
(3) Set of isosceles
right triangles (4) Set of right angled
triangles
Answer:
(3) Set of isosceles right triangles
19. The shaded region in
the Venn diagram is
(1) Z −(X ÈY) (2) (X È Y) Ç Z
(3) Z −(X ÇY) (4) Z È (X ÇY)
Answer:
(3) Z – (X ∩ Y)
20. In a city, 40% people
like only one fruit, 35% people like only two fruits, 20% people like all the
three fruits. How many percentage of people do not like any one of the above
three fruits?
(1) 5 (2)
8
(3) 10 (4)
15
Answer:
(1) 5
The
Venn Diagram gives you a clear idea of this question.
40
+ 35 + 20 + x = 100%
95%
+ x = 100%
x
= 5%
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