Sets
Get insights from 131 questions on Sets, answered by students, alumni, and experts. You may also ask and answer any question you like about Sets
- 131
Questions
- 0
Discussions
- 1
Active Users
- 2
Followers
Have a question about Sets? Ask our experts
Keep it short & simple. Type complete word. Avoid abusive language.
37. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that
(i) A B) = A ∩ B
(ii) A ∩ B) = A B
37. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that
(i) A B) = A ∩ B
(ii) A ∩ B) = A B
37. (i) L.H.S = (A B) = U – (A B)
= {1,2,3,4,5,6,7,8,9} – [ {2,4,6,8) {2,3,5,7}]
= {1,2,3,4,5,6,7,8,9} – {2,3,4,5,6,7,8}
= {1,9}
R.H.S. = A ∩ B = [U – A] ∩ [U B]
= ∩
= {1,3,5,7,9} ∩ {1,4,6,8,9}
= {1,9}
? L.H.S. = R.H.S.
(A B) = A ∩ B.
(ii) L.H.S. = (A ∩ B) = U – (A ∩ B)
= {1,2,3,4,5,6
Upvote 
36. Taking the set of natural numbers as the universal set, write down the complements of the following sets:
(i) {x : x is an even natural number}
(ii) { x : x is an odd natural number }
(iii) {x : x is a positive multiple of 3}
(iv) { x : x is a prime number }
(v) {x : x is a natural number divisible by 3 and 5}
(vi) {x : x is a perfect square }
(vii) { x : x is a perfect cube}
(viii) {x : x + 5 = 8 }
(ix) { x : 2x + 5 = 9}
(x) {x : x 7} (xi) { x : x N and 2x + 1 > 10 }
36. Taking the set of natural numbers as the universal set, write down the complements of the following sets:
(i) {x : x is an even natural number}
(ii) { x : x is an odd natural number }
(iii) {x : x is a positive multiple of 3}
(iv) { x : x is a prime number }
(v) {x : x is a natural number divisible by 3 and 5}
(vi) {x : x is a perfect square }
(vii) { x : x is a perfect cube}
(viii) {x : x + 5 = 8 }
(ix) { x : 2x + 5 = 9}
(x) {x : x 7} (xi) { x : x N and 2x + 1 > 10 }
3. (i) {x : x is an odd natural number}
(ii) {x : x is an even natural number}
(iii) {x : x is not a multiple of 3}
(iv) {x : x is a positive composite number and x = 1}
(v) {x : x is a natural number not divisible by 3 and 5}.
(vi) {x : x is not a perfect square}
(vii) {x : x is not a perfect c
Upvote 35. If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets :
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g} (iv) D = { f, g, h, a}
35. If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets :
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g} (iv) D = { f, g, h, a}
35. (i) A = U – A = {a, b, c, d, e, f, g, h} – {a, b, c}
= {d, e, f, g, h}
(ii) B = U – B = {a, b, c, d, e, f, g, h} – {d, e, f, g}
= {a, b, c, h}.
(iii) C = U – C = {a, b, c, d, e, f, g, h} – {a, c, e, g}.
= {b, d, f, h}
(iv) D = U – D = {a, b, c, d, e, f, g, h} – {f, g, h, a}
= {b, c, d, e}
Upvote Exercise 1.5 Class 11 Maths Solutions
34. Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = { 1, 2, 3, 4}, B = { 2, 4, 6, 8 } andC = { 3, 4, 5, 6 }. Find
(i) A
(ii) B
(iii) (A C)
(iv) (A B)
(v) (A )
(vi) (B – C)
Exercise 1.5 Class 11 Maths Solutions
34. Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = { 1, 2, 3, 4}, B = { 2, 4, 6, 8 } andC = { 3, 4, 5, 6 }. Find
(i) A
(ii) B
(iii) (A C)
(iv) (A B)
(v) (A )
(vi) (B – C)
34. (i) A = U – A = {1,2,3,4,5,6,7,8,9} – {1,2,3,4}
= {5,6,7,8,9}
(ii) B = U – B = {1,2,3,4,5,6,7,8,9} – {2,4,6,8}
= {1,3,5,7,9}.
(iii) (A C) = A ∩ C
= {5,6,7,8,9} ∩ [U – C] [? (i)]
= {5,6,7,8,9} ∩ [ {1,2,3,4,5,6,1,8,9} – {3,4,5,6}]
= {5,6,7,8,9} ∩ {1,2,7,8,9}
= {7,8,9}
(iv) A B) = A ∩ B [By demorgan
Upvote 33. State whether each of the following statement is true or false. Justify your answer.
(i) {2, 3, 4, 5} and {3, 6} are disjoint sets.
(ii) {a, e, i, o, u} and {a, b, c, d}are disjoint sets.
(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.
33. State whether each of the following statement is true or false. Justify your answer.
(i) {2, 3, 4, 5} and {3, 6} are disjoint sets.
(ii) {a, e, i, o, u} and {a, b, c, d}are disjoint sets.
(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.
33. (i) False, as {2,3,4,5} ∩ {3,6} = {3} ≠ .Hence sets are not disjoint.
(ii) False as {a, e, i, o, u} ∩ {a, b, c, d} = {a} ≠ Hence sets are not disjoint.
(iii) True as {2,6,10,14} ∩ {3,7,11,15} = . Hence sets are disjoint.
(iv) True as {2,6,10} ∩ {3,7,11}= .
Upvote 32. If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?
32. If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?
32. R – Q = {x: x is a real number but not rational number}
= {x: x is an irrational number}
Since real number = rational number + irrational number
Upvote 31. If X= { a, b, c, d } and Y = { f, b, d, g}, find
(i) X – Y
(ii) Y – X
(iii) X ∩ Y
31. If X= { a, b, c, d } and Y = { f, b, d, g}, find
(i) X – Y
(ii) Y – X
(iii) X ∩ Y
31. (i) X – Y = {a, b, c, d} – (f, b, d, g}
= {a, c}
(ii) Y – X = {f, b, d, g} – {a, b, c, d}
= {f, g}
(iii) X ∩ Y = {a, b, c, d} ∩ {f, b, d, g}
= {b, d}.
Upvote 30. If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find
(i) A – B
(ii) A – C
(iii) A – D
(iv) B – A
(v) C – A
(vi) D – A
(vii) B – C
(viii) B – D
(ix) C – B
(x) D – B
(xi) C – D
(xii) D – C
30. If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find
(i) A – B
(ii) A – C
(iii) A – D
(iv) B – A
(v) C – A
(vi) D – A
(vii) B – C
(viii) B – D
(ix) C – B
(x) D – B
(xi) C – D
(xii) D – C
30. (i) A – B = {3,6,9,12,15,18,21} – {4,8,12,16,20}
= {3,6,9,15,18,21}
(ii) A – C = {3,6,9,12,15,18,21} – {2,4,6,8,10,12,14,16}
= {3,9,15,18,21}
(iii) A – D = {3,6,9,12,15,18,21} – {5,10,15,20}
= {3,6,9,12,18,21}
(iv) B – A = {4,8,12,16,20} – {3,6,9,12,15,18,21}
= {4,8,16,20}
(v) C – A = {2,4,6,8,10,1
Upvote 29. Which of the following pairs of sets are disjoint
(i) {1, 2, 3, 4} and {x : x is a natural number and }
(ii) {a, e, i, o, u } and { c, d, e, f }
(iii) {x : x is an even integer} and {x : x is an odd integer}
29. Which of the following pairs of sets are disjoint
(i) {1, 2, 3, 4} and {x : x is a natural number and }
(ii) {a, e, i, o, u } and { c, d, e, f }
(iii) {x : x is an even integer} and {x : x is an odd integer}
29. (i) {1,2,3,4} ∩ {x : x is a natural number and 4 ≤ x ≤ 6}
{1, 2, 3, 4} ∩ {4, 5, 6}
{4} ≠∅
Hence, the given pair of set is not disjoint.
(ii) {a, e, i, o, u} ∩ {c, d, e, f}
{e} ≠∅
Hence, the given pair of set is not disjoint.
(iii) {x: x is an even integer} ∩ {x: x is are odd integer}.
=∅
As
Upvote 28. If A = {x : x is a natural number }, B = {x : x is an even natural number}
C = {x : x is an odd natural number} and D = {x : x is a prime number }, find
(i)A B
(ii) A C
(iii) A D
(iv) B C
(v) B D
(vi) C D
28. If A = {x : x is a natural number }, B = {x : x is an even natural number}
C = {x : x is an odd natural number} and D = {x : x is a prime number }, find
(i)A B
(ii) A C
(iii) A D
(iv) B C
(v) B D
(vi) C D
28. A = {1,2,3,4,5, 6, …}
B = {2,4,6, …}
C = {1,3,5, …}
D = {2,3,5, …, }
(i) A ∩ B = {1,2,3,4 …} ∩ {2,4,6, …} = {2,4,6 …} = B.
(ii) A ∩ C = {1,2,3,4, …} ∩ {1,3,5 …} = {1,3,5, …} = C.
(iii) B ∩ C = {2,4,6, …} ∩ {1,3,5, …} = .
(iv) B ∩ D = {2,4,6 …} ∩ {2,3,5 …} = {2}
(v) C ∩ D = {1,3,5, …} ∩
Upvote