Set of odd natural numbers divisible by 2 isn’t a null set
Hide | ShowAnswer :
False
Set of even prime numbers is an null set
Hide | ShowAnswer :
False
{x:x is a natural numbers, x < 3 and x > 11 } is an finite set
Hide | ShowAnswer :
True
{z:z is a point common to any two parallel lines} is an finite set
Hide | ShowAnswer :
True
The set of months of a leap year is a infinite set
Hide | ShowAnswer :
False
{0,1, 2, 3, 4 ...} is a infinite set
Hide | ShowAnswer :
True
{1, 2, 3 ... 99} is an finite set
Hide | ShowAnswer :
True
The set of positive integers greater than 9 is an finite set
Hide | ShowAnswer :
False
The set of lines which are parallel to the x-axis is an finite set
Hide | ShowAnswer :
False
The set of letters in the English alphabet is a infinite set
Hide | ShowAnswer :
False
The set of natural numbers under 200 which are multiple of 7 is infinite set
Hide | ShowAnswer :
False
The set of animals living on the earth is a infinite set
Hide | ShowAnswer :
False
The set of circles passing through the origin (0, 0) is a infinite set
Hide | ShowAnswer :
True
The set A = {-2, -3}; B = {x: x is solution of x2 + 5x + 6 = 0} are not equal sets
Hide | ShowAnswer :
False
The set P = {x: x is a letter in the word FOLLOW}; Q = {y: y is a letter in the word WOLF} are equal sets
Hide | ShowAnswer :
True
{2, 3, 4} ⊄ {1, 2, 3, 4, 5}
Hide | ShowAnswer :
False
{a, b, c}⊂ {b, c, d}
Hide | ShowAnswer :
False
{x: x is a student of Class X of your school} ⊂ {x: x student of your school}
Hide | ShowAnswer :
True
{x: x is a square in the plane} ⊂ {x: x is a rectangle in the same plane}
Hide | ShowAnswer :
True
{p: p is a triangle in a plane}⊄ {p: p is a rectangle in the plane}
Hide | ShowAnswer :
True
Find the smallest set X such that X∪{1, 2}={1, 2, 3, 5, 9}.
Hide | ShowAnswer :
We have to find the smallest set X such that X∪{1, 2}={1, 2, 3, 5, 9}.
The union of the two sets X & Y is the set of all those elements that belong to X or to Y or to both X & Y.
Thus, X must be {3, 5, 9}.
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, P = {2, 4, 6, 8} and Q = {2, 3, 5, 7}. Verify that
(i) (A∪B)'=A'∩B'
(ii) (A∩B)'=A'∪B'.
Answer :
Given:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, P = {2, 4, 6, 8} and Q = {2, 3, 5, 7}
We have to verify:
(i) (P∪Q)'=P'∩Q'
LHS
P∪Q ={2,3,4,5,6,7,8} (P∪B )'={1,9}
RHS
P'={1,3,5,7,9} Q'={1,4,6,8,9} P'∩Q'={1,9}
LHS = RHS
Hence proved.
(ii) (P∩Q)'=P'∪Q'
LHS
P∩Q={2} (P∩Q)'={1,3,4,5,6,7,8,9}
RHS
P'={1,3,5,7,9} Q'={1,4,6,8,9} P'∪Q'={1,3,4,5,6,7,8,9}
LHS = RHS
Hence proved.
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, P = {1, 2, 3, 4}, Q= {2, 4, 6, 8} and R = {3, 4, 5, 6}. Find
(i) P'
(ii) Q'
(iii) (P∩R)'
(iv) (P∪Q)'
(v) (P')'
(vi) (Q−R)'
Hide | Show
Answer :
Given:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, P = {1, 2, 3, 4}, Q= {2, 4, 6, 8} and R = {3, 4, 5, 6}
(i) P' = {5, 6, 7, 8, 9}
(ii) Q' = {1, 3, 5, 7, 9}
(iii) (P∩R)' = {1, 2, 5, 6, 7, 8, 9}
(iv) (P∪Q)' = {5, 7, 9}
(v) (P')' = {1, 2, 3, 4} = A
(vi) (Q−R)' = {1, 3, 4, 5, 6, 7, 9}
Let P = {3, 6, 12, 15, 18, 21}, Q = {4, 8, 12, 16, 20}, R = {2, 4, 6, 8, 10, 12, 14, 16} and S = {5, 10, 15, 20}. Find:
(i) P−Q
(ii) P−R
(iii) P−S
(iv) Q−P
(v) R−P
(vi) S−P
(vii) Q−R
(viii) Q−S
Answer :
Given:
P = {3, 6, 12, 15, 18, 21}, Q = {4, 8, 12, 16, 20}, R = {2, 4, 6, 8, 10, 12, 14, 16} and S = {5, 10, 15, 20}
(i) P−Q = {3, 6, 15, 18, 21}
(ii) P−R = {3, 15, 18, 21}
(iii) P−S = {3, 6, 12, 18, 21}
(iv) Q−P = {4, 8, 16, 20}
(v) R−P = {2, 4, 8, 10, 14, 16}
(vi) S−P = {5, 10, 20}
(vii) Q−R = {20}
(viii) Q−S = {4, 8, 12, 16}
Let P={x:x∈N}, B={x:x−2n, n∈N}, C={x:x=2n−1, n∈N} and D = {x : x is a prime natural number}. Find:
(i) P∩Q
(ii) P∩R
(iii) P∩S
(iv) Q∩R
(v) Q∩S
(vi) R∩S
Answer :
P={x:x∈N}={1,2,3,...} Q={x:x−2n, n∈N}={2,4,6,8,...} R={x:x=2n−1, n∈N}={1,3,5,7,...} S = {x:x is a prime natural number.} = {2, 3, 5, 7,...}
(i) P∩Q = Q
(ii) P∩R = R
(iii) P∩S = S
(iv) B∩R = ϕ
(v) B∩S = {2}
(vi) R∩S = S−{2}
If P = {1, 2, 3, 4, 5}, Q = {4, 5, 6, 7, 8}, R = {7, 8, 9, 10, 11} and S = {10, 11, 12, 13, 14}, find:
(i) P∪Q
(ii) P∪R
(iii) Q∪R
(iv) Q∪S
(v) P∪Q∪R
(vi) P∪Q∪S
(vii) Q∪R∪S
(viii) P∩Q∪R
(ix) (P∩Q)∩(Q∩R)
(x) (P∪S)∩(Q∪R)
Answer :
Given:
P = {1, 2, 3, 4, 5}, Q = {4, 5, 6, 7, 8}, R = {7, 8, 9, 10, 11} and S = {10, 11, 12, 13, 14}
(i) P∪Q = {1, 2, 3, 4, 5, 6, 7, 8}
(ii) P∪R = {1, 2, 3, 4, 5, 7, 8, 9, 10, 11}
(iii) Q∪R = {4, 5, 6, 7, 8, 9, 10, 11}
(iv) Q∪S = {4, 5, 6, 7, 8, 10, 11, 12, 13, 14}
(v) P∪Q∪R = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
(vi) P∪Q∪S = {1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14}
(vii) Q∪R∪S = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
(viii) P∩(Q∪R) = {4, 5}
(ix) (P∩Q)∩(Q∩R) = ϕ
(x) (P∪S)∩(Q∪R) = {4, 5, 10, 11}
Answer :
From the Venn diagrams given below, we can clearly say that if X and Y are two sets such that X⊂Y, then
(i) Form the given Venn diagram, we can see that X∩Y = X
(ii) Form the given Venn diagram, we can see that X∪Y = Y
If P = {1, 2, 3, 4, 5}, Q = {4, 5, 6, 7, 8}, R = {7, 8, 9, 10, 11} and S = {10, 11, 12, 13, 14}, find:
1 |
Q∪S |
A |
{1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14} |
2 |
P∪Q∪R |
B |
{4, 5, 6, 7, 8, 10, 11, 12, 13, 14} |
3 |
P∪Q∪S |
C |
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} |
Answer :
1-B, 2-C, 3-A
sets in Roster form
1 |
{x ∈ R : x > x}. |
A |
{17, 26, 35, 44, 53, 62, 71, 80} |
2 |
{x : x is a prime number which is a divisor of 60} |
B |
Φ |
3 |
{x : x is a two digit number such that the sum of its digits is 8} |
C |
{T, R, I, G, O, N, M, E, Y} |
4 |
The set of all letters in the word 'Trigonometry' |
D |
{2, 3, 5} |
Answer :
1-B, 2-D, 3-A, 4-C
sets in Roster form
1 |
{x : x is a letter before e in the English alphabet} |
A |
{1, 2, 3, 4} |
2 |
{x ∈ N : x2 < 25} |
B |
{11, 13, 17, 19} |
3 |
{x ∈ N : x is a prime number, 10 < x < 20} |
C |
{a, b, c, d} |
4 |
{x ∈ N : x = 2n, n ∈ N} |
D |
{2, 4, 6, 8, 10,...} |
Answer :
1-C, 2-A, 3-B, 4-D
If P = {1, 2, 3, 4, 5}, Q = {4, 5, 6, 7, 8}, R = {7, 8, 9, 10, 11} and S = {10, 11, 12, 13, 14}, find:
1 |
P∪Q |
A |
{1, 2, 3, 4, 5, 6, 7, 8} |
2 |
P∪R |
B |
{4, 5, 6, 7, 8, 9, 10, 11} |
3 |
Q∪R |
C |
{1, 2, 3, 4, 5, 7, 8, 9, 10, 11} |
Answer :
1-A, 2-C, 3-B
sets in set-builder form
1 |
A = {1, 2, 3, 4, 5, 6} |
A |
{x:x∈N, 9<x<16} |
2 |
B={1, ½ , 1/3 , ¼ , 1/5, ...} |
B |
{x:x∈N, x<7} |
3 |
C = {0, 3, 6, 9, 12, ...} |
C |
{x: x=1n, x∈N} |
4 |
D = {10, 11, 12, 13, 14, 15} |
D |
{x:x=3n, n∈Z+} |
Answer :
1-B, 2-C, 3-D, 4-A
The GSEB Books for class 10 are designed as per the syllabus followed Gujarat Secondary and Higher Secondary Education Board provides key detailed, and a through solutions to all the questions relating to the GSEB textbooks.
The purpose is to provide help to the students with their homework, preparing for the examinations and personal learning. These books are very helpful for the preparation of examination.
For more details about the GSEB books for Class 10, you can access the PDF which is as in the above given links for the same.