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If A And B Are Two Equivalence Relations Defined On The Set C Then

Solution: (1) If A and B are equivalence relations, then A ∩ B is an equivalence relation.... View Article

If R Is The Set Of Real Numbers Then Statement I A X Y R R Y X Is An Integer Is An Equivalence Relation On R

If R is the set of real numbers. Then, Statement I: A = {(x, y) ∈ R × R : y - x is an integer} is an equivalence relation on R.... View Article

If R Is A Relation On The Set N Defined By X Y 2x Y 10 Then R Is

Solution: (4) {(x, y) : 2x - y = 10} 20 ∈ N but (20, 20) ∉ R It is not reflexive. (20, 30) ∉ R, but (30, 20) ∉ R It... View Article

If Z Is The Set Of Integers Then The Relation R A B 1 Ab 0 On Z Is

Solution: (3) 1 + ab > 0 ab > -1 Reflexive {a, a} → a2 > -1 → a ∈ R Symmetric {a, b} → ab > -1 {b, a} →... View Article

For Any Two Real Numbers Theta And Phi We Define Theta R Phi If And Only If Sec 2 Theta Tan 2 Phi 1 The Relation R Is

For any two real numbers θ and ϕ, we define θRϕ, if and only if sec2 θ - tan2ϕ = 1. The relation R is (1) reflexive but not... View Article

If S Is The Set Of All Real Numbers A Relation R Has Been Defined On S By Arb A B 1 Then R Is

If S is the set of all real numbers. A relation R has been defined on S by aRb ⇔ |a - b| ≤ 1 then R is (1) symmetric and transitive but... View Article

If R Is A Relation On The Set A Then Find The Relation

Solution: (3) A = {3, 6, 9,12} R = {(3, 3), (6, 6), (9, 9), (12,12), (6, 12), (3, 9), (3,12), (3, 6)} R is reflexive but not symmetric. (a,... View Article

If Sets A And B Are Defined As A X Y Y 1 X 0 X R And B X Y Y X X R Then

If sets A and B are defined as A = {(x, y): y = (1 / x), 0 ≠ x ∈ R} and B = {(x, y): y = -x, x ∈ R}, then (1) A ∩ B = A (2) A... View Article

If A B Then B A Is Equal To

If A ⊆ B, then B ∪ A is equal to (1) B ∩ A (2) A (3) B (4) None of these Solution: (3) Given that A ⊆ B, B ∪ A = B.... View Article

In A Class Of 30 Pupils 12 Take Chemistry 16 Take Physics And 18 Take History

Solution: (1) Total number of pupils = 30 Number of pupils taking Chemistry = n (C) = 12 Number of pupils taking Physics = n (P) = 16 Number... View Article

N N 1 2n 1 N Z Is A Subset Of

Solution: (1) The value of n becomes n = ± 1. A = {...... -30, 0, -6, 6, 30,.....} A = {6K : K ∈ Z}... View Article

The Number Of Elements In The Set A B 2 A 2 3 B 2 35 A B Z Where Z Is The Set Of All Integers Is

Solution: (3) 2a2 + 3b2 = 35 3b2 = 35 - 2a2 Maximum value on RHS is 35. 3b2 ≤ 35 b2 ≤ 11.66 b = 0, ± 1, ± 2, ±... View Article

If N A 4 N B 3 And N A B C 24 Then N C Is Equal To

Solution: (5) n (A × B × C) = n (A) × n (B) × n (C) 24 = 3 × 4 × n (C) 24 = 12 × n (C)... View Article

If A X X Is A Multiple Of 3 And B X X Is A Multiple Of 5 Then A Intersection B Is Given By

Solution: (3) Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, .... A = {3, 6, 9, 12, 15, 18, 21, ....} Multiples of 5 = 5, 10, 15, 20, 25, 30 ....... View Article

If A X Y Then The Power Set Of A Is

Solution: (4) A = {x, y} Power set contains all the sets of values of A and all subsets of A. Power set of A = {ɸ, {x}, {y}, {x, y}}.... View Article

If X And Y Are The Sets Of All Positive Divisors Of 400 And 1000 Respectively Including 1

Solution: (5) The factors of 400 and 1000 are given below. 400 = 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 1000 = 1, 2, 4, 5,... View Article

If A 1 2 3 4 And B 2 4 6 Then The Number Of Set C Such That A Intersection B C A Union B Is

If A = {1, 2, 3, 4} and B = {2, 4, 6}. Then, the number of set C such that A ∩ B ⊆ C ⊆ A ∪ B is (1) 6 (2) 9 (3) 8 (4) 10 (5) 12... View Article

If Universal Set Is Given Then Find A Intersection B Is Equal To

Solution: (3) U = x5 - 6x4 + 11x3 - 6x2 = 0 U = x2 (x3 − 6x2 + 11x − 6) U = x2 (x − 1) (x − 2) (x − 3) A... View Article

Is A Intersection Of A Is Phi

Solution: (2) A ∩ ϕ = ϕ ϕ denotes an empty set. The intersection of an empty set is an empty set.... View Article

If Z Denotes The Integers A And B Are Given Then Find The Number Of Element In A Intersection B

Solution: (5) A = {(a, b):a2 + 3b2 = 28, a, b ∈ Z} A = {(1, 3), (-1, 3}, (4, 2}, (- 4, 2}, (5, 1), (-5, 1), (-5, -1), (-4, -2), (-1, -3),... View Article