# CBSE Solutions for Class 11 Maths

#### Select CBSE Solutions for class 10 Subject & Chapters Wise :

Set of odd natural numbers divisible by 2 isn’t a null set

False

Set of even prime numbers is an null set

False

{x:is a natural numbers, < 3 and > 11 } is an finite set

True

{z:is a point common to any two parallel lines} is an finite set

True

The set of months of a leap year is a infinite set

False

{0,1, 2, 3, 4 ...} is a infinite set

True

{1, 2, 3 ... 99} is an finite set

True

The set of positive integers greater than 9 is an finite set

False

The set of lines which are parallel to the x-axis  is an finite set

False

The set of letters in the English alphabet is a infinite set

False

The set of natural numbers under 200 which are multiple of 7 is infinite set

False

The set of animals living on the earth is a infinite set

False

The set of circles passing through the origin (0, 0) is a infinite set

True

The set A = {-2, -3}; B = {xis solution of x2 + 5+ 6 = 0} are not equal sets

False

The set P = {xis a letter in the word FOLLOW}; Q = {yis a letter in the word WOLF} are  equal sets

True

{2, 3, 4} ⊄ {1, 2, 3, 4, 5}

False

{abc}⊂  {bcd}

False

{xis a student of Class X of your school} ⊂  {xstudent of your school}

True

{xis a square in the plane} ⊂  {xis a rectangle in the same plane}

True

{pis a triangle in a plane}⊄  {pis a rectangle in the plane}

True

Find the smallest set X such that X∪{1, 2}={1, 2, 3, 5, 9}.

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'.

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)'

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

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

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)

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}

If X and Y are two sets such that XY, then find:
(i) X∩Y
(ii) XY

From the Venn diagrams given below, we can clearly say that if X and Y are two sets such that XY, then
(i) Form the given Venn diagram, we can see that  X∩Y = X
(ii) Form the given Venn diagram, we can see that  XY = 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}

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}

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,...}

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}

1-A, 2-C, 3-B

sets in set-builder form

 1 A = {1, 2, 3, 4, 5, 6} A {x:x∈N, 9