CLASS XI (MATHEMATICS)
HOLIDAY HOMEWORK
(Q1) Write each of following sets in roster method?
(i) Set of factors of 8
(ii) A={x: x=5y-1,y ∈ N,Y >3}
(iii)B={x: x ∈ I and -5 < x < 2}
(iv)C={(x, y): x, y € N and x = y}
(v)D= {2x :x ∈ W and x is prime}
(vi)E={x:x ∈ z and |x| ≤ 2}
(vii)F={x:x is a two digit number such that sum of its two digits is 9}
(viii)G={x ∈ R :x > x}
(Q2) Write each of following sets using sets builder form
(i)A={3,6,9,12....}
(ii)A={ , , , ….}
(iii)A={April, June, September, November}
(iv)A={ 0 }
(v)A={5,-5}
(vi)A={ , ,
,
,
,
,
}
(Q3) if A,B and C are three sets such that A ⊂ B and B ⊂ C then prove that A ⊂ C.
(Q4) Write all possible subset sof
(i){a}
(ii){5,7}
(iii){0,1,2}
(Q5) If A is any set prove that A ⊆ ∅ ⇔
(iv){0}
= ∅
(Q6)How many subsets and proper subset has a set of
(i) 5 elements
(ii) 8 elements
(Q7) If A = {2x: n ∈ N},B={3x: x ∈
} and C ={
(i) ∩ (iii) n elements
; ∈
}
∩ ∩
∩ ∪
∩
(Q8) Express each of the following by venn diagram
(i)(A∪
∪ ∪
∩ (iv) ∩
(vii)
∪
T
− (viii) A ∪ At
−
(ix) A ∩ At
(x) A ∪ ∅
Q9) A and B are two sets such that n(A)=3 and n(B)= 6,find:(i) minimum value of n(A U B)
(ii)maximum value of n(A U B)
(Q10) Write A U B and A ∩ B if
(i) ⊂ !"
#$" %&' !$"
=
!" #$$()*+%$*
(Q11) Write all sets of all positive integer s whose cube is odd
(Q12) Prove every set is subset of itself
(Q13)Prove empty set is subset of every set
{
}
(Q14)If x = 4 n − 3n − 1 : n ∈ N and Y = {9(n − 1) : n ∈ N }. Prove X ⊂ Y.
(Q15)Let A ={a,b,c,d},B={a,b,c} and C={b,d}, find all sets X such that
(i)X ⊂
!", ⊂ -
(ii), ⊂ !", ⊄
(Q16)If A and B are sets, then prove that (A-B),(A ∩
and (B – A) are pairwise disjoint.
(Q17) Let A,B and C be three sets such that A U B = C and ∩
= ∅, */$!)#' $*/ *A = C-B
(Q18) For any two sets A and B , prove that A’- B’= B – A
(Q19)If n (U) = 25, n(A) =15,!
∩
= ,!
(i) n(B)
0
1
= 8 then find
(ii)n(B – A)
(Q20) There are two sets of players A and B. In set A there are 20 players and in B there are11
players, How many elements will there be in (a) A U B (b) A ∩ if
(i) no players of set A is a player of B
(ii) 8 players of set A are players of set B
(iii) all players of set B are also players of set A
(Q21) The population of the town is 6000, out of these 3400 persons read Hindustan times and
2700 persons read times of india .There are 700 persons who read both the papers .Find the
number of persons who do not read either of two papers.