## Kerala Plus One Maths Chapter Wise Previous Questions and Answers Chapter 1 Sets

Question 1.

If A and B are events such that ;;

a. P(A or B)

b. P(not A and not B) [March-2018]

Answer:

Question 2.

a. If A={a, b, c}, then write Power Set P(A).

b. If the number of subsets with two elements of a set P is 10, then find the total number of elements in set P.

c. Find the number of elements in the power set of P. [March-2018]

Answer:

a. P(A) = {F, {a}, {b}, {c}, {a,b}, {b,c}, {a,c}, {a,b,c}}

b. ^{n}C_{2} = 10

Question 3.

Consider Venn diagram of the Universal Set

U = {1,2,3,4,5,6,7,8,9,10,11,12,13}

a. Verify (A∪B)’ = A’∩B’

b. Find n(A∩B)’ [March-20181

Answer:

a. A={3,4,6,10} B= {2,3,4,5,11}

b. (A∪B)’ = {1,7, 8, 9, 12, 13}

A’ = { 1, 2, 5, 7, 8, 9, 11, 12, 13}

B’ = {1, 6, 7, 8, 9, 10, 12, 13 }

A’∩B’ = {l,7, 8, 9, 12, 13}

∴ (A∪B)’=A’∩B’

c. n(A∩B)’ = n(U)-n(A∩B)=13-2 = 11

Question 4.

If U is the universal set and A is any set then U∩A = …………

i. U

ii. A

iii. φ

iv. A’

Consider the sets

U = {a,b,c,d,e,f,g}.

A = {b,c,d,e} and

B = {a,c,g}.

Find A’ and B’ and then verify that (A∪B)’ =A’∩B’ .

c. In a group of 400 people, 250 can speak Hindi and 200 can speak Malayalam. How many people can speak both Hindi and Malayalam? [March-2017]

Answer:

No. of people who speak both Hindi and Malayalam =- 50

Question 5.

a. If A is a subset of the set B, then

A∩B = ………….

b. Represent the above set A∩B by Venn diagram.

c. In a school, there are 20 teachers who teach Mathematics or Physics. Of these, 12 teach .Mathematics. 12 teach Physics. How many teach both the subjects? [March-2016]

Answer:

a. A

c. Let M = set of teachers, who teach Mathematics.

P = set of teachers, who teach Physics;

n(M) = 12, n (P) = 12: n(M ∪ P) = 20

.’. n (M∩P) = n(M) + n (P) – n (M ∪ P)= 12+12-20 = 4

Question 6.

Let A = {x : x∈W. x <5}, B = {x : x is a prime number less than 5} and U = {x : x is an integer, 0 < x < 6}.

a. Write A, Band U in roster form.

b. Find (A-B) ∪ (B-A)

c. Verify (A∪B)’ = A’∩B’. [March-2015]

Answer:

a. A= {0,1,2,3,4}, B = {2,3}

U= {0,1,2,3,4,5,6}

Question 7.

Consider the sets A = {2, 3, 5, 7} and B = {1,2,3,4,6,12}

a Find A∩B

b. Find A-B,B-A and hence show that (A∩B) ∪ (A-B) ∪ (B-A) = A ∪ B

c. Write the power set of A ∩ B.

Answer:

Question 8.

If U = {1,2,3,4,5,6,7,8,9},

A = {1,2,4,7} and B = {1,3,5,7}

a Find A∪B.

b. Find A’, B’ and hence show that (A∪B)’ =A’∩ B’

c. The power set P(A∪B) has……. elements. [March-2013]

Answer:

U= {1,2,3,4,5,6,7,8,9},

A= {1,2,4,7} and B= {1,3,5,7}

Question 9.

Consider sets U, A and B given by

U = {x: x is a natural number < 8}

A = {x: x is a prime number < 6}

B = {x: x is a odd number < 9}

i. Write U, A and B in the roster form.

ii. Find A’, B’, (A∪B) and A∩B [February-2013]

Answer:

i.U= {1,2,3,4,5,6,7},

A={2,3,5} and B= {1,3,5,7}

ii. A’={1,4,6,7} B’ = {2,4,6}

A∪B= {1,2,3,5,7}

A∩B= {3,5}

Question 10.

Let A= {x : x is an integer, 1/2 < 7/2}

B = {2,3,4}

a Write A in the roster form,

b. Find the power set of (A∪ B)

c. Verify that(A-B)∪(A∩B)=A

A={x:x is a whole number, 1/2<x<7/2}

B = {2,3,4} [March-2012]

Answer:

a. Let A= {1,2,3}

b. A∪B= {1,2,3,4}

P(A∪B)={l}, {2},{3}, {4},_{(}{1,2}, {1,3}, {1,4}, {2, 3},{2, 4}, {3, 4}, {1,2,3},

{1,2,4}, {2,3,4}, {1,3,4}, {1,2,3,4}, {φ} = 24= 16 elements

c. A-B={1},A∩B={2,3}

(A- B)∪(A∩B)= {1,2,3} = A

Question 11.

Consider the sets A and B given by

A = {x: x is a prime number < 10}

B = {x: x is a natural number which divides 12}

i. Write A and B in the roster form.

ii. Find A∪B and A-B

iii. Verify that (A∪B)-A=B-A [March-2011]

Answer:

i.A= {2,3,5,7}; B = {1,2,3,4,6,12}

ii. A∪B = {1,2,3,4,5,6,7,12}

B-A= {1,4,6,12}

iii. (A∪B) – A= (1,4,6,12} = B – A

Question 12.

A={x:x is a natural number 2< x < 6}

B = {x: x is a prime number x < 7}

C = {x: x^{2} – 5x + 6 = 0}

i. Write A, B, C in the roster form.

ii. Verify that (A∪B)∪C=A∪(B ∪C) [March-2010]

Answer:

Question 13.

Which among the following is a finite set?

a. {x : x is an integer less than 1}

b. {x : x is an integer which is divisible by 7}

c. {x: x is a prime numberless than 9^{10}}

d {x : x R ∩ Q : R, set of real numbers, Q, set of rational numbers} [Say-2010]

Answer:

c. {x: x is a prime number less than 9^{10}}

Question 14.

If A = {1}, B = {{1}, 2}, C = {{1}, 3} and U= {{1}, {2}, {3}, 1,2,3} then find

a. A∩B

b. B∩C

c. n[(A∩B)’ ∪ (B∩C)’]

Answer:

Question 15.

Let A={x∈ R,x^{2}-5x + 6 = 0} and B = {x: x ∈ R, x^{2} = 9}

i. Write A and B in roster form

ii. Find (A∪B) and (A∩B)

iii. Find A-B, B-A and verify that

(A- B) ∪ (B – A) = (A∪ B) – (A∩B) [August-2009]

Answer:

i.A= {2,3},B= {-3,3}

ii. A∪B = {-3,2,3}, (A∩B) = {3}

iii. A- B = {2}, B – A= {-3}

LHS = {2, -3} = RHS

Question 16.

Let U = {1,2,3,4,5,6,7,8}, A={2,4,6,8} and B = {2,4,8} .Find A’and B’

a. Find A’and B’

b. Also find (A∪B)’

c. Verify (A∪B)’= A’ n B’ [March- 2009]

Answer:

a.

A’ =U-A= {1,3,5,7}, .

B’ = U-B= {1,3,5,6,7}

b. A∪B= {2,4,6,8}

(A∪B)’ = U-(A∪B)= {1,3,5,7}

c. A’∩B’={l,3,5,7},

(A∪B)’={1,3,5,7} ‘

∴ (A∪B)’ = A’∩B’

Question 17.

Let V={a,e,i,o,u} and B={a,i, k,u}. Find V-B and B – V. [September-2008]

Answer:

V-B= {e,o}, B-V = {k}

Question 18.

i. If X = {a, b, c, d} and Y = {f,b,d,g} then find X-Y and X∩Y ,

ii. State whether the following is true or false: If A⊂B, then A∪B = B. [February – 2008]

Answer:

i.X.-Y={a,c}, X∩Y={b,d}

ii True

Question 19.

For two sets A and B, with A∩B’ = φ, which among the following is true.

[A = φ; B⊂A;A’⊂B; A⊂B] [September-2007]

Answer:

A⊂B ( y A∩B’ = (φ ⇒A⊂B)

Question 20.

Write all the subsets of the set {-1,0,1} [June-2007]

Answer:

{-1), {0} {1}

{-1,0,1} {-1,0}, {-1,1}

{0,1} φ