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The Relation R Defined On The Set Of Natural Numbers As A B A Differs From B By 3 Is Given By

Solution: (2) Given: a differs from b by 3 a - 3 = b a = b + 3 If N = 1, 2, 3, 4… b = 1, a = 4 b = 2, a = 5 b = 3, a = 6 The relation... View Article

If R Is An Equivalence Relation On A Set A Then R 1 Is

Solution: (3) A = {a, b, c} R: {(a, a}, (b, b), (c, c), (a, b), (b, a), (a, c), (c, a), (b, c), (c, a)} R-1 = {(a, a}, (b, b), (c, c), (b,... View Article

If R 3 3 6 6 9 9 12 12 6 12 3 9 3 12 3 6 Is A Relation On The Set A 3 6 9 12 Then The Relation Is

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 R 1 3 4 2 2 4 2 3 3 1 Is A Relation On The Set A 1 2 3 4 Then Relation R Is

Solution: (3) R = {(1,3), (4, 2), (2, 4), (2, 3), (3, 1) A = {1, 2, 3, 4} Reflexive: (1, 1), (2, 2), (3, 3), (4, 4) ∈ R Transitive: (a,... View Article

On The Set N Of All Natural Numbers Define The Relation R By Arb If And Only If The Gcd Of A And B Is 2 Then R Is

Solution: (2) aRb ⇒ GCD of a and b is 2 Reflexive: (a, a) ∈ R aRa ⇒ GCD (a, a) = a (3, 3) ∉ R (4, 4) ∉ R Symmetric (a, b) ∈ R ⇒ GCD (a,... View Article

If R Is A Relation From 11 12 13 To 8 10 12 Defined By Y X 3 Then R 1 Is Equal To

Solution: (1) R = {y = x - 3} x = 11, y = 8 x = 12, y = 9 x = 13, y = 10 The ordered pairs are (11, 8), (13, 10). (12, 9) is not an... View Article

If A 1 2 3 And B 2 3 4 Then Which Of The Following Relations Is A Function From A To B

Solution: (3) Choice 3 satisfies the condition of a given function. Hence, {(1, 3), (2, 3), (3, 3)} is a function.... View Article

R Is A Relation On N Given By R X Y 4x 3y 20 Which Of The Following Belongs To R

Solution: (4) 4x + 3y = 20 x = 5, y = 0 x = 3, 12 + 3y = 20 3y = 8 y = 8 / 3 x = 2, 8 + 3y = 20 3y = 12 y = 4 x = (2, 4) is the only... View Article

If R Is A Relation Defined As Arb Iff A B 0 Then The Relation Is

Solution: (4) R is a relation defined as aRb, iff |a - b| > 0 Reflexive: aRa, iff |a − a| > 0 is not true R is not reflexive.... View Article

If R Is The Real Line Consider The Following Subsets Of The Plane R R S X Y Y X 1 And 0 X 2 T X Y X Y Is An Integer Which One Of The Following Is Correct

Solution: (1) If x is a real number, x − x = 0 ∈ set of integers I (x, x) ∈ T It is reflexive. (x, y) ∈ T; (y, x) ∈ T x − y = I; y − x ∈ I... View Article

If A Relation R On The Set N Of Natural Numbers Is Defined As X Y X 2 4xy 3y 2 0 X Y N

Solution: (1) x2 - 4xy + 3y2 = 0 (x - y) (x - 3y) = 0 (a, a) ∈ R (a - a) (a - 3a) = 0 Relation is reflexive (a, b) ∈ R (b, a) ∈ R (3,... View Article

If R Is A Relation From R Set Of Real Numbers To R Defined By R A B A B R And A B Root 3 Is An Irrational Number Then The Relation R Is

Solution: (1) a ∈ R a - a + √3 = √3 is an irrational number (a, a) ∈ R R is reflexive. a, b ∈ R a - b + √3 is an irrational number b - a... View Article

If R And S Are Two Non Void Relations On A Set A Then Which Of The Following Statements Is Incorrect

Solution: (2) Consider A = {a, b, c} R: A → A S: A → A If R and S are reflexive, R ⋃ S is reflexive. R ⋂ S is reflexive If R & S are... View Article

If A X Y Z And B A B C D Then Which One Of The Following Is Not A Relation From A To B

Solution: (4) A = {x, y, z} B = {a, b, c, d} {(z, b), (y, b), (a, d)} is not a relation from A to B.... View Article

Consider The Relations R X Y X Y Are Real Numbers And X Wy For Some Rational Number W S M N P Q M N P And Q Are Integers Such That N Q 0 And Qm Pn Then

Solution: (3) R: x = wy (0, a) ∈ R a = wa w = 1 not equal Given that S = (m / n, p / q) and mq = np Hence qn = pm Also mn = pq (ab, ab) ∈ S S is... View Article

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