Archives

Let A A B C B B C D C A B D E Then A Intersection B Union C Is

1) {a, b, c} 2) {b, c, d} 3) {a, b, d, e} 4) {e} Solution: (1) (B ⋃ C) = {a, b, c, d, e} A ∩ (B ⋃ C) = {a, b, c} ∩ {a, b, c, d, e} A ∩... View Article

If A B C Be Three Sets Such That A Union B A Union C And A Intersection B A Intersection C Then

1) A = B 2) B = C 3) A = C 4) A = B = C Solution: (2) A ⋃ B = A ⋃ C (A ⋃ B) ∩ C = (A ⋃ C) ∩ C (A ∩ C) ⋃ (B ∩ C) = C [(A ⋃ C) ∩ C = C]... View Article

Let A 1 2 3 4 B 2 4 6 Then Find The Number Of Sets C Such That A B C A B

1) 6 2) 9 3) 8 4) 10 Solution: (3) A = {1, 2, 3, 4} B = {2, 4 , 6} A ∩ B ⊆ C ⊆ A ⋃ B {2, 4} ⊆ C ⊆ {1, 2, 3, 4, 6} C = (2, 4), (1, 2,... View Article

Let X And Y Be The Sets Of All Positive Divisors Of 400 And 1000 Respectively Including 1 And The Number Then N X Intersection Y

1) 4 2) 6 3) 8 4) 12 Solution: (4) The factors of 400 and 1000 are given below. 400 = 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100,... View Article

For Any Two Sets A And B A A B Equals

1) B 2) A – B 3) A ∩ B 4) Ac ∩ Bc Solution: (3) A – (A – B) = A ∩ B... View Article

Let A And B Be Two Sets Then

1) A ⋃ B ⊆ A ⋂ B 2) A ⋂ B ⊆ A ⋃ B 3) A ⋂ B = A ⋃ B 4) None of these Solution: (2) A ⋂ B ⊆ A ⊆ A ⋃ B Therefore, A ⋂ B ⊆ A ⋃ B... View Article

If A And B Are Two Sets Then A Union B A Intersection B Iff

1) A ⊆ B 2) B ⊆ A 3) A = B 4) None of these Solution: (3) Let x ∈ A ⇒ x ∈ A ⋃ B, [Because A ⊆ A ⋃ B] x ∈ A ⋂ B, [As A ⋃ B = A ⋂ B] x ∈ A... View Article

If A Intersection B B Then

1) A ⊂ B 2) B ⊂ A 3) A = ɸ 4) B = ɸ Solution: (2) Since A ⋂ B = B Therefore, B ⊂ A.... View Article

The Smallest Set A Such That A 1 2 1 2 3 5 9 Is

1) {2,3,5} 2) {3,5,9} 3) {1,2,5,9] 4) None of these Solution: (2) A ⋂ {1, 2} = ɸ then A will be the smallest A = {1, 2, 3, 5, 9} - {1, 2}... View Article

The Number Of Non Empty Subsets Of The Set 1 2 3 4 Is

1) 15 2) 14 3) 16 4) 17 Solution: (1) The given set contains 4 elements. The number of non-empty subsets = 2n - 1 = 24 - 1 = 16 - 1 = 15... View Article

If N A 8 And N A Intersection B 2 Then N A Intersection B Dash A Is Equal To

1) 2 2) 4 3) 6 4) 8 5) 10 Solution: (3) n [(A ⋂ B’) ⋂ A] = n [(A’ ⋃ B’) ⋂ A] = n (A’ ⋂ A) ⋃ n (B’ ⋂ A)... View Article

Which Set Is The Subset Of All Given Sets

1) {1,2,3,4,...} 2) {1} 3) {0} 4) {} Solution: (4) Null set is the subset of all given sets.... View Article

If Q X X 1 Y Where Y Belongs To N Then

1) 0 ϵ Q 2) 1 ϵ Q 3) 2 ϵ Q 4) (2 / 3) ∈ Q Solution: (2) As (1 / y) ≠ 0, (1 / y) ≠ 2, (1 / y) ≠ (2 / 3), (1 / y) ≠ (- 2 / 3) (1 / y) can be 1.... View Article

A X X X Represents

1) {0} 2) {} 3) {1} 4) {x] Solution: (2) It is basic concept that a null set is defined as, A = {x : x = x} = {}.... View Article

The Function F 0 3 1 29 Defined By F X 2x 3 15x 2 36x 1 Is

1) One - one and onto 2) onto but not one - one 3) one - one but not onto 4) neither one-one nor onto Solution: (2) f (x) = 2x3 - 15x2 +... View Article

If P Q And R Are Subsets Of Set A Then R P C Union Q C C

1) (R x P) ⋂ (R x Q) 2) (R x Q) ⋂ (R x P) 3) (R x P) ⋃ (R x Q) 4) None of these Solution: (2) R x (Pc ⋃ Qc)c = R x [(Pc)c ⋂ (Qc)c] = R... View Article

If A A B B C D C D E Then A C A D A E B C B D B E Is Equal To

1) A ⋂ (B ⋃ C) 2) A ⋃ (B ⋂ C) 3) A x (B ⋃ C) 4) A x (B ⋂ C) Solution: (3) (B ⋃ C) = {c, d, e} A ⋂ (B ⋃ C) = ɸ A ⋃ (B ⋃ C) = {a, b, c ,d,... View Article

If The Set A Has P Elements B Has Q Elements Then The Number Of Elements In A B Is

1) p + q 2) p + q + 1 3) p q 4) p2 Solution: (3) n (A x B) = n (A) x n (B) = p x q = pq... View Article

For A Belongs To R The Set Of All Real Numbers A 1 1 60 Then A

1) 5 2) 7 3) - 15 / 2 4) - 17 / 2 Solution: (2) a = 7 or (-17 / 2) Since a < 0, diverges, a = 7.... View Article

If Two Sets A And B Are Having 99 Elements In Common Then The Number Of Elements Common To Each Of The Sets A B And B A Are

1) 299 2) 992 3) 100 4) 18 5) 9 Solution: (2) n (A ∩ B) = 99 (A × B) ⋂ (C × D) = (A ∩ C) × (B ∩ D) (A × B) ⋂ (B × A) = (A ∩ B) × (B... View Article