Contents
Andhra Pradesh SSC Class 10 Solutions For Maths – Sets (English Medium)
These Solutions are part of AP SSC Class 10 Solutions for Maths. In this article, we have provided Andhra Pradesh SSC Class 10 Solutions For Maths Chapter 2 Sets.
Exercise 2.1:
Question 1:
Which of the following are sets? Justify your answer.
- The collection of all the months of a year begining with the letter “J”.
- The collection of ten most talented writers of India.
- A team of eleven best cricket batsmen of the world.
- The collection of all boys in your class.
- The collection of all even integers.
Solution :
- It is well defined so it is a set.
- The collection is not well defined so it is not a set.
- The collection is not well defined, so it is not a set.
- We get same collection, so the collection forms a well defined set.
- The collection of all even integers gets same collection, so the collection forms a well defined set.
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Question 2:
If A={0,2,4,6}, B = {3,5,7} and C = {p, q, r}then fill the appropriate symbol, ∈ or ∉ in the blanks.
- 0…… A
- 3…… C
- 4…… B
- 8…… A
- p…… C
- 7…… B
Solution :
- 0 ∈ A (Since 0 is an element of A)
- 3 ∉ C (Since 3 is not an element of C)
- 4 ∉ B (Since 4 is not an element of B)
- 8 ∉ A (Since 8 is not an element of A)
- p ∈ C (Since p is an element of C)
- 7 ∈ B (Since 7 is an element of B)
Question 3:
Express the following statements using symbols.
- The elements V does not belong to ‘A’.
- ‘d’ is an element of the set ‘B’.
- ‘l’ belongs to the set of Natural numbers N.
- ‘8’ does not belong to the set of prime numbers P
Solution :
- X ∉ A
- d ∈ B
- 1 ∈ N
- 8 ∉ P
Question 4:
State whether the following statements are hue or false. Justify your answer
- 5 ∉ set of prime numbers
- S = {5, 6, 7} implies 8 ∈ S.
- -5 ∉ W where 4 ‘W’ is the set of whole numbers
- 8/11 ∈ Z where ‘Z’ is the set of integers.
Solution :
- False-5 can only be divided evenly by 1 or 5, so it is a prime number.
- False-8 does not belong to the set of prime numbers S.
- True
- False- An integer is number with no fractional part.
Question 5:
Write the following sets in roster form.
- B = {x: x is a natural number smaller than 6}
- C = {x: x is a two-digit natural number such that the sum of its digits is 8}.
- D = {x : x is a prime number which is a divisor of 60}.
- E = {x : x is an alphabet in BETTER}.
Solution :
- B={1,2,3,4,5}
- C={17,26,35,44,53,62,71}
- D={5,3}
- E={B,E,T,R}
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Question 6:
Write tine following sets in the set-builder form.
- {3, 6, 9, 12}
- {2,4, 8, 16, 32}
- {5, 25, 125, 625}
- {1 ,4, 9, 16, 25, ……..100}
Solution :
- A={x : x is multiple of 3 and less than 13}
- B={x : x is in power of 2xand x is less than 6}
- C={x : x is in power of 5 and x is less than 5}
- D={x : x is square of natural number and not greater than 10}
Question 7:
Write tine following sets in roster form.
- A= {x : x is a natural number greater than 50 but smaller than 100}
- B = {x : x is an integer, x2 = 4}
- D = {x : x is a letter in the word “LOYAL”}
Solution :
- A ={51,52,53,54,55,56,………..,98,99}
- B ={-2,2}
- D={L, A, O, Y}
Question 8:
Solution :
- {1, 2, 3, 6}= {x : x is a natural number and divisor of 6}
- {2, 3}= x : x is prime number and a divisor of 6}
- {M, A, T, H, E, I, C, S} = {x : x is a letter of the word MATHEMATICS}
- {1,3,5,7,9}= {x : x is an odd natural number less than10}
Exercise 2.2:
Question 1:
If A= {1,2, 3,4}; B= {1,2, 3,5,6} then find A∩ B and B ∩ A. Are they equal?
Solution :
- Not empty.
- Empty set – An odd number is an integer that is not evenly divisible by 2.
- Empty set – There is no natural number less than 5 and greater than 7
- Empty set- The definition of parallel lines is exactly those two lines are parallel if and only if they have no common points.
- Not empty.
Question 2:
A= {0,2,4}, find A∩ ∅ and A∩A. Comment.
Solution :
- If the counting process of a elements of a set terminates then such a set is finite set.The set contain the month of year such as {January, Feb, March, April, May …December}. Hence, it is finite set.
- If the counting process of a elements of a set terminates then such a set is finite set. Hence, the set contain all the natural number from 1 to 100.
- If the counting process of a elements of a set terminates then such a set is finite set. Hence, the set of the prime numbers less than 99 is finite.
Question 3:
If A= {2, 4, 6,8, 10} and B= {3, 6, 9, 12, 15}, find A-B and B-A.
Solution :
- If the counting process of a elements of a set terminates then such a set is finite set. Therefore, the given set is finite set.
- A set which is not finite is infinite set. Therefore, the given set is infinite set.
- A set which is not finite is infinite set. Therefore, the given set is infinite set.
- A set which is not finite is infinite set. Therefore, the given set is infinite set.
Exercise 2.3:
Question 1:
Which of the following sets are equal?
- A = {x : x is a letter in the word FOLLOW}
- B = {x : x is a letter in the word FLOW}
- C = {x : x is a letter in the word WOLF}
Solution :
All the three sets A, B and C have same elements so the three sets are equal.
Question 2:
Consider the following sets and fill up the blank in the statement given below with = or ≠ so as to make the statement true.
Solution :
- If A and B contain the same elements, they are equal. A = B
- If A and E do not contain the same elements, they are equal A ≠ E
- If C and D contain the same elements, they are equal. C = D
- If D and F do not contain the same elements, they are equal D ≠ F.
- If F and A do not contain the same elements, they are equal. F≠ A
- If D and E do not contain the same elements, they are equal.D≠ E
- If F and B do not contain the same elements, they are equal. F ≠ B.
Question 3:
In each of the following, state whether A = B or not.
- A = {a, b, c, d,} B = {d, c, a, b}
- A = {4, 8, 12, 16} B = {8, 4, 16, 18}
- A = {2, 4, 6, 8, 10} B = {x : x is a positive even integer and x<10}
- A = {x : x is a multiple of 10} B = {10, 15, 20, 25, 30}
Solution :
- If A and B contain the same elements, they are equal. A = B
- If A and B do not contain the same elements, they are equal. A ≠ B
- If A and B contain the same elements, they are equal A= B
- If A and B do not contain the same elements, they are equal. A ≠ B
Exercise 2.4:
Question 1:
State which of the following sets are empty and which are not?
- The set of lines passing through a point.
- Set of odd natural numbers divisible by 2.
- {x : x is a natural number, x < 5 and x > 7}
- {x: x is a common point to any two parallel lines}
- Set of even prime numbers.
Solution :
- True
- True
- False
- False
Question 2:
Which of the following sets are finite or infinite.
- The set of months in a year.
- {1, 2, 3, …, 99, 100}
- The set of prime numbers smaller than 99.
Solution :
- {1, 2, 3,…..,10} ≠ {2, 3,4,5……,9}
- {x:x= 2n+1 and x ∈ N}=2x+1 means x is odd {2, 4, 6, 8,10} ≠ {x:x = 2n+1 and x ∈ N}
- {x:x is a multiple of 15}= {15, 30, 45}, so 5 does not exist.
{5,15,30,45} ≠ {x:x is a multiple of 15} - x: x is a prime number, but 9 is not a prime number.
{2,3,5,7,9} ≠ {x:x is a prime number}
Question 3:
State whether each of the following sets is finite or infinite.
- The set of letters in the English alphabet.
- The set of lines which are parallel to the X-Axis.
- The set of numbers which are multiplies of 5.
- The set of circles passing through the origin (0,0).
Solution :
- B = {p, q}
Subsets are: {p}, {q}, {p, q}, {ϕ} - C={x, y, z}
Subsets are:{x}, {y},{z}, {x, y}, {y, z}, {z, x}, {x, y, z}, { ϕ} - D={a, b, c, d}
Subsets are: {a}, {b},{c}, {d}, {a, b}, {b, c},
{c, d}, {a, c}, {a, d}, {b, d}, {a, b, c}, {b, c, d}, {a, c, d}, {a, b, d},{a, c, b , d}, { ϕ} - E={1, 4, 9, 16}
Subsets are: {1}, {4}, {9}, {16}, {1, 4}, {1, 9}, {1, 16}, {4, 9}, {4, 16}, {9, 16}, {1, 4, 9}, {1, 9, 16}, {4, 9, 16}, {1, 4, 16}, {1, 4, 9,16},{ ϕ } - F={10, 100, 1000}
Subsets are: {10}, {100}, {1000}, {10,100}, {10, 1000}, {100, 1000}, {10, 100, 1000}, { ϕ }.
Exercise 2.5:
Question 1:
Solution :
The common element in both A and B are 1, 2, 3.
A ∩ B = {1, 2, 3}
B ∩ A = {1, 2, 3}
Therefore, A ∩ B = B ∩ A
Question 2:
Solution :
As we, know the intersection of two sets is the set of all elements which are common to both sets.
A ∩ ϕ = ϕ
A ∩ A = A
Question 3:
Solution :
Given,
A = {2, 4, 6, 8, 10}
B = {3, 6, 9, 12, 15}
So,
A – B = {2, 4, 8, 10}, only element which are in A but not in B should be taken.
Similarly for B-A, the elements which are only in B are taken.
∴ B – A = {3, 9, 12, 15}.
Question 4:
Solution :
Given A ⊂ B so all the element of A are in B,
∴ A ∪ B = B.
Question 5:
Solution :
Given:
A= {1, 2, 3, 4, 5, 6…..}
B= {2, 4, 6, 8, 10……..}
C= {1, 3, 5, 7, 9, 11…}
D= {2, 3, 5, 7, 11, 13…}
- A ∩ B= {even natural number} = {2, 4, 6…}
- A ∩ C= {odd natural number}= {1, 3, 5, 7..}
- A ∩ D= {4, 6, 8, 10, 12,………100}
- B ∩ C= ϕ
- B ∩ D={even prime number}={2}
- C ∩ D={odd prime number}= {3, 5, 7, 11, 13,…..97}
*Remark: The answer given at the end of the textbook is incorrect.
Question 6:
Solution :
- A – B = {3, 6, 9, 15, 18, 21}
- A – C ={3, 9, 15, 18, 21}
- A – D ={3, 6, 9,12, 18, 21}
- B – A = {4, 8, 16, 20}
- C – A = {2, 4, 8, 10, 14, 16}
- D – A = {5, 10, 20}
- B – C = {20}
- B – D = {4, 8, 12, 16}
- C – B = {2, 6, 10, 14}
- D – B = {5, 10, 15}
Question 7:
Solution :
- False, because they have common element ‘3’.
- False, because they have common element ‘a’.
- True, because no common elements for the sets.
- True, because they have no common elements.
Hope given Andhra Pradesh SSC Class 10 Solutions For Maths chapter 2 Sets are helpful to complete your math homework.
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