Sets and Relation questions
385 published questions with worked solutions.
- Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more...
- 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 x R y if and only if 2x 3y. Let be the number of elements in R, and...
- 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...
- 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 be the number of elements in R. Let...
- 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. Given below are two...
- 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...
- Let X = R × R. Define a relation R on X as: (a_1, b_1) R (a_2, b_2) b_1 = b_2. Statement-I: R is an equivalence relation....
- 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 ^2x - ^2y = 1. Then R is :
- Let S = N 0 . Define a relation R from S to R by : R = (x,y): _e y = x _e ( 2 5 ), x S, y R Then, the sum of all the elements in...
- Let A = 1, 2, 3,...., 100 and R be a relation on A such that R = (a, b): a = 2b + 1 . Let (a_1, a_2), (a_2, a_3), (a_3, a_4), ,...
- Let A be the set of all function 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 = –2, –1, 0, 1, 2, 3 . Let R be a relation on A defined by xRy if and only if y = x, 1 . Let l be the number of elements in...
- Let A = 0, 1, 2, 3, 4, 5 . Let R be a relation on A defined by (x, y) R if and only if max x, y 3, 4 . Then among the statements...
- 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...
- Let A and B be two sets, then (A B)' (A' B) is equal to
- For any two sets A and B, if A X=B X= and A X=B X for some set X, then (AMU 2009)
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