A well defined collection of objects or ideas is known as a set. If
(i) All the objects of the collection have the common property and
(ii) It is possible to decide whether the given object belongs to the
collection or not then the collection is said to be well-defined and
is defined as a set.
Multiple Choice Questions:
1. If A = {1, 2, 3, 4, 5} which of the following are not correct?
i. 4 e A ii. 6 e A iii. 5 e A iv. 7 e A
A) i & ii B) ii & iii C) iii & iv D) i & iv
2. Null set is represent as ......
i. φ ii. {0} iii. { } iv. {φ}
A) i & ii B) i & iii C) i, ii & iii D) ii, iii & iv
3. The number of subsets of the Set C = {x, y, z} are ......
A) 2 B) 3 C) 6 D) 8
4. A = {a, e, i} B = {x / x is a vowel in the word 'Mathematics'}
C = {a, e, i, o, u}
Which of the sets A, B & C are equal sets?
A) A & B B) B & C C) A & C D) A, B & C
Answers: 1-C; 2-B; 3-D; 4-A.
10th Class Maths Important Questions - New Syllabus - Sets Chapter for AP and Telangana
Q: Take any two sets of your choice to prove
i) AU B = B U A
ii) A ∩ B = B ∩ A.
Hint: As you are given choice to select two sets write any two sets A
and B and try to prove the relations. For example:
Solution: A = {1, 2, 3, 4, 5}
B = {3, 4, 5, 6, 7}
i) AU B = {1, 2, 3, 4, 5} U {3, 4, 5, 6, 7}
= {1, 2, 3, 4, 5, 6, 7}
BUA = {1, 2, 3, 4, 5, 6, 7}
A U B = B U A
ii) A ∩ B = {3, 4, 5}
B ∩ A = {3, 4, 5}
A ∩ B = B ∩ A
Q: From the given venn diagram, find
1) X U Y 3) X − Y
2) X ∩ Y 4) Y − X
What can you infer about X . Y, X n Y and X - Y?
Hint: Write the sets in roster form and answer the given questions. As
X Y, X - Y will be the empty set.
Solution: X = {2, 4}
Y = {1, 2, 3, 4, 5}
1) X . Y = {1, 2, 3, 4, 5} = Y
2) X n Y = {2, 4} = X
3) X - Y = {2, 4} - {1, 2, 3, 4, 5}= { }
4) Y - X = {1, 2, 3, 4, 5} - {2, 4} = {1, 3, 5}
X - Y is an empty set as X Y.
Q: Sneha has taken two sets of her choice and observed that n (A . B)
= n (A) + n (B). Jhansi argued that
n (A . B) = n (A) + n (B) - n (A n B). Who is correct? Give your reasons.
Hint: Jhansi's statement is correct for any two sets A and B. And
Sneha's statement is correct when the sets A and B are disjoint.
Solution: If the sets A and B are disjoint n (A n B) = 0
n (A . B) = n (A) + n(B)
This shows that Sneha has considered two disjoint sets.
But, for any two sets A and B
n (A . B) = n (A) + n (B) - n (A n B) is always true.
Jhansi's statement is true for any two sets A and B.
And Sneha's statement is conditionally true i.e., for only two disjoint sets.
Q: If n (A − B) = 10 and n (B − A) = 20 and n (A U B) = 45 then find n (A ∩ B).
Hint: This problem can be solved easily using a venn diagram.
Solution:
n (A U B) = n (A − B) + n (A ∩ B) + n (B − A)
45 = 10 + n (A ∩ B) + 20
n (A ∩ B) = 45 − 30 = 15
Q: Which of the following sets are infinite. Try to impose a condition
to make them finite.
i) A = {2, 4, 6, 8, ...}
ii) B = {a, e, i, o, u}
iii) C = {..., −3, −2, −1, 0, 1, 2, 3, ...}
Hint: You have many options to impose conditions to make the infinite
Sets A and C finite.
Solution:
Sets A and C are infinite sets as the elements of these sets are infinite.
i) A = {2, 4, 6, 8, ...}
The elements of Set A are multiples of 2. If the elements of Set A are
considered as the multiples of 2 less than 10 then it becomes finite.
ii) C = {..., −3, −2, −1, 0, 1, 2, 3, ....}
The elements of Set C are integers. If the elements of Set C are taken
as the integers that lie between −5 and 5 it becomes finite.
i) AU B = B U A
ii) A ∩ B = B ∩ A.
Hint: As you are given choice to select two sets write any two sets A
and B and try to prove the relations. For example:
Solution: A = {1, 2, 3, 4, 5}
B = {3, 4, 5, 6, 7}
i) AU B = {1, 2, 3, 4, 5} U {3, 4, 5, 6, 7}
= {1, 2, 3, 4, 5, 6, 7}
BUA = {1, 2, 3, 4, 5, 6, 7}
A U B = B U A
ii) A ∩ B = {3, 4, 5}
B ∩ A = {3, 4, 5}
A ∩ B = B ∩ A
Q: From the given venn diagram, find
1) X U Y 3) X − Y
2) X ∩ Y 4) Y − X
What can you infer about X . Y, X n Y and X - Y?
Hint: Write the sets in roster form and answer the given questions. As
X Y, X - Y will be the empty set.
Solution: X = {2, 4}
Y = {1, 2, 3, 4, 5}
1) X . Y = {1, 2, 3, 4, 5} = Y
2) X n Y = {2, 4} = X
3) X - Y = {2, 4} - {1, 2, 3, 4, 5}= { }
4) Y - X = {1, 2, 3, 4, 5} - {2, 4} = {1, 3, 5}
X - Y is an empty set as X Y.
Q: Sneha has taken two sets of her choice and observed that n (A . B)
= n (A) + n (B). Jhansi argued that
n (A . B) = n (A) + n (B) - n (A n B). Who is correct? Give your reasons.
Hint: Jhansi's statement is correct for any two sets A and B. And
Sneha's statement is correct when the sets A and B are disjoint.
Solution: If the sets A and B are disjoint n (A n B) = 0
n (A . B) = n (A) + n(B)
This shows that Sneha has considered two disjoint sets.
But, for any two sets A and B
n (A . B) = n (A) + n (B) - n (A n B) is always true.
Jhansi's statement is true for any two sets A and B.
And Sneha's statement is conditionally true i.e., for only two disjoint sets.
Q: If n (A − B) = 10 and n (B − A) = 20 and n (A U B) = 45 then find n (A ∩ B).
Hint: This problem can be solved easily using a venn diagram.
Solution:
n (A U B) = n (A − B) + n (A ∩ B) + n (B − A)
45 = 10 + n (A ∩ B) + 20
n (A ∩ B) = 45 − 30 = 15
Q: Which of the following sets are infinite. Try to impose a condition
to make them finite.
i) A = {2, 4, 6, 8, ...}
ii) B = {a, e, i, o, u}
iii) C = {..., −3, −2, −1, 0, 1, 2, 3, ...}
Hint: You have many options to impose conditions to make the infinite
Sets A and C finite.
Solution:
Sets A and C are infinite sets as the elements of these sets are infinite.
i) A = {2, 4, 6, 8, ...}
The elements of Set A are multiples of 2. If the elements of Set A are
considered as the multiples of 2 less than 10 then it becomes finite.
ii) C = {..., −3, −2, −1, 0, 1, 2, 3, ....}
The elements of Set C are integers. If the elements of Set C are taken
as the integers that lie between −5 and 5 it becomes finite.
IPE Hyderabad Admissions into PG Diploma in Management Programme 2014
Institute of Public Enterprise (IPE), Hyderabad is inviting applications from eligible candidates for admissions into Post Graduate Diploma in Management Programme for the academic session 2014.
Courses : Post Graduate Diploma in Management Programme
Duration of programme : Two-year full-time
Eligibility : Bachelor's Degree with minimum 50 percent marks in aggregate.
Selection procedure : Based on merit in Admission Test (CAT / MAT / ATMA / XAT / CMAT / JMET).
Duly filled in application form along with relevant documents should reach the Institute of Public Enterprise. Last date for the receipt of filled in application form is 31st December, 2014.
Courses : Post Graduate Diploma in Management Programme
Duration of programme : Two-year full-time
Eligibility : Bachelor's Degree with minimum 50 percent marks in aggregate.
Selection procedure : Based on merit in Admission Test (CAT / MAT / ATMA / XAT / CMAT / JMET).
Duly filled in application form along with relevant documents should reach the Institute of Public Enterprise. Last date for the receipt of filled in application form is 31st December, 2014.
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