Sets and Relation questions
385 published questions with worked solutions.
- Suppose set A consists of first 250 natural numbers that are multiples of 3 and set B consists of first 200 even natural numbers....
- Let R_ 1 and R_ 2 be two relations defined on R by a R_ 1 b ab 0 and a R_ 2 b a b. Then,
- For N, consider a relation R on N given by R = (x, y) : 3x + y is a multiple of 7 . The relation R is an equivalence relation if...
- Let R_ 1 = (a, b) N N : |a − b| 13 and R_ 2 = (a, b) N N : |a − b| 13 . Then on N:
- Let R_ 1 and R_ 2 be relations on the set 1, 2, _____, 50 such that R_ 1 = (p, p^ n ) : p is a prime and n 0 is an integer and R_...
- Let R be a relation from the set 1, 2, 3, _____, 60 to itself such that R = (a, b) : b = pq, where p, q 3 are prime numbers ....
- The probability that a relation R from x, y to x, y is both symmetric and transitive, is equal to
- Let a set A = A_ 1 A_ 2 … A_k, where A_ i A_ j = for i j, 1 i, j k. Define the relation R from A to A by R = (x, y) : y A_ i if...
- Suppose X= 1, 2, 3, 4 and R is a relation on X. If R= (1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2) , then which one of...
- A relation R is defined on the set N of natural numbers as xRy x^2-4xy+3y^2=0. Then which one of the following is correct?
- Consider the following statements for the two non-empty sets A and B : 1. (A B) (A B ) ( A B)=A B 2. (A ( A B ))=A B Which of the...
- Let X be a non-empty set and let A, B, C be subsets of X. Consider the following statements : 1. A C (A B) (C B), (A B) (C B) 2....
- If A= , , , then the power set of A is
- Let A = x R : [x + 3] + [x + 4] 3 , B = x R:3^x ( _ r=1 ^ 3 10^r )^ x-3 <3^ -3x , where [f] denotes greatest integer function....
- 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...
- Let A = 1, 2, 3, 4, 5, 6, 7 . Then the relation R = (x, y) A A : x + y = 7 is
- Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of A × B each having at least...
- 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 odd positive integer or x...
- Let A = 2, 3, 4 and B = 8, 9, 12 . Then the number of elements in the relation R= ((a_1,b_1),(a_2,b_2)) (A B,A B):a_1 divides b_2...
- 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 = (a_1,b_1),(a_2,b_2)) : a_1 b_2...
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