Relations: JEE Questions & Solutions

The number of relations, defined on the set a, b, c, d, which are both reflexive and symmetric, is equal to:

Let A = 2, 3, 5, 7, 9. Let R be the relation on A defined by xRy if and only if 2x 3y. Let l be the number of elements in R, and m be the…

Let the relation R on the set M = 1, 2, 3,, 16 be given by R = (x, y): 4y = 5x - 3, x, y M. Then the minimum number of elements required to…

Let A = -2, -1, 0, 1, 2, 3, 4. Let R be a relation on A defined by xRy if and only if 2x + y 2. Let l be the number of elements in R. Let m…

Let A = 0, 1, 2,..., 9. Let R be a relation on A defined by (x, y) R if and only if |x - y| is a multiple of 3. Statement I: n(R) = 36.…

Let R be a relation defined on the set 1,2,3,4 1,2,3,4 by R= ((a,b),(c,d)): 2a+3b=3c+4d Then the number of elements in R is

The number of non-empty equivalence relations on the set 1,2,3 is:

Let A = 1,2,3. The number of relations on A, containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is.

Let R = (1, 2), (2, 3), (3, 3) be a relation defined on the set 1, 2, 3, 4. Then the minimum number of elements needed to be added in R so…

Let X = R R. Define a relation R on X as: (a1, b1) R (a2, b2) b1 = b2. Statement-I: R is an equivalence relation. Statement-II: For some…

The relation R = (x, y): x, y Z and x + y is even is:

Define a relation R on the interval [ 0, 2 ] by x R y if and only if ^2 x - ^2 y = 1. Then R is:

Let A be the set of all functions f: Z Z and R be a relation on A such that R = (f, g): f(0) = g(1) and f(1) = g(0) Then R is:

Let A = 1, 2, 3,, 10 and R be a relation on A such that R = (a, b): a = 2b + 1. Let (a1, a2), (a3, a4), (a5, a6),, (ak, ak+1) be a sequence…

Let A = -3,-2,-1,0,1,2,3. Let R be a relation on A defined by xRy if and only if 0 x^2 + 2y 4. Let l be the number of elements in R and m…

Let A = -2, -1, 0, 1, 2, 3. Let R be a relation on A defined by (x, y) R if and only if |x| |y|. Let m be the number of reflexive elements…

Let A = -3, -2, -1, 0, 1, 2, 3 and R be a relation on A defined by xRy if and only if 2x - y 0, 1. Let l be the number of elements in R.…

The number of relations on the set A = 1, 2, 3 containing at most 6 elements including (1, 2), which are reflexive and transitive but not…

Let A = 0, 1, 2, 3, 4, 5. Let R be a relation on A defined by (x, y) R if and only if x, y 3, 4. Then among the statements (S1): The number…

Let S = 1,2,3...10. M is the set of all subsets, and relation R = (A,B): A B=. R is:

Let R be a relation on Z Z defined by (a, b)R(c, d) if and only if ad - bc is divisible by 5. Then R is:

If R is the smallest equivalence relation on the set 1, 2, 3, 4 such that (1, 2), (1, 3) R, then the number of elements in R is:

The number of symmetric relations defined on the set 1, 2, 3, 4 which are not reflexive is:

Let A = 1, 2, 3, 4 and R = (1, 2), (2, 3), (1, 4) be a relation on A. Let S be the equivalence relation on A such that R S and the number…

Let A = 1, 2, 3, 4, 5. Let R be a relation on A defined by xRy if and only if 4x 5y. Let n be the number of elements in R and m be the…

The minimum number of elements that must be added to the relation R = (a, b), (b, c), (b, d) on the set a, b, c, d so that it is an…

Let R be a relation defined on N as a R b if 2a + 3b is a multiple of 5. Then R is:

The minimum number of elements that must be added to the relation R = (a, b), (b, c) on the set a, b, c so that it becomes symmetric and…

Let R be a relation on N N defined by (a, b) R (c, d) if and only if ad(b - c) = bc(a - d). Then R is:

Among the relations S = (a, b): a, b R 0, a^2 + b^2 0 And T = (a, b): a, b R, a^2 - b^2 Z which of the following is true?

Let R be a relation on R, given by R = (a, b): 3a - 3b + 7 is an irrational number Then R is:

Let P(S) denote the power set of S = 1, 2, 3,, 10. Define the relations R1 and R2 on P(S) as A R1 B if (A B^c) (B A^c) =, and A R2 B if A…

Statement (P Q) (R Q) is logically equivalent to:

Let A = 1,2,3,4,,10 and B = 0,1,2,3,4. The number of elements in the relation R = (a,b) A A: 2(a-b)^2 + 3(a-b) B is:

Among the statements: (S1): () () is a tautology. (S2): () () is a contradiction. Choose the correct answer from the options given below:

Let A = 0, 3, 4, 6, 7, 8, 9, 10 and R be the relation defined on A such that R = (x, y) A A: x - y is an odd positive integer or x - y = 2.…

Let A = 2, 3, 4 and B = 8, 9, 12. Then the number of elements in the relation R = ((a1, b1), (a2, b2)) (A B, A B): a1 divides b2 and a2…

Let A = 1, 3, 4, 6, 9 and B = 2, 4, 5, 8, 10. Let R be a relation defined on A B such that R = ((a1, b1), (a2, b2)): a1 b2 and b1 a2. Then…

The number of relations, on the set 1, 2, 3 containing (1, 2) and (2, 3), which are reflexive and transitive but not symmetric, is:

Section – B Let A = -4, -3, 2, 0, 1, 3, 4 and R = (a, b): a A, b = |a| or a = b be a relation on A. Then the minimum number of elements…

Let A= 1,2,3,4 and R be a relation on the set A A defined by R= ((a,b),(c,d)): 2a+3b=4c+5d Then the number of elements in R is