The relation S is defined on the set of integers Z as xSy if integer x – InterviewSolution

InterviewSolution

1.	The relation S is defined on the set of integers Z as xSy if integer x devides integer y. ThenA. s is an equivalence relationB. s is only reflexive and symmetricC. s is only reflexive and transitiveD. s is only symmetric and transitive
Answer» Correct Answer - C The relation S is defined on the set of integers Z and xSy, if integer x divides integery. Reflexive : Since, every integer divides itself `therefore` integer x divides integer x implies xSx Hence, S is reflexive. Symmetric : Let `x, y in Z` such that xSy i.e., integer x divides integer y Now, this does not implies that integer y divides integer x. e.g. Take x = 2 and y = 4 Then, 2 divides 4 but 4 does not divides 2. Thus, S is not symmetric. Transitive : Let `x, y, z in Z` such that xSy and ySz. implies integer x divides integer y and integer y divides integer z implies integer x divides integer z implies xSz Hence, S is transitive.

Discussion

No Comment Found

Related InterviewSolutions

If A and B are two sets such that n (A ∪ B) = 50, n (A) = 28 and n (B) = 32, find n (A ∩ B).
The solution of `8x = 6 (mod 14)` isA. [8],[6]B. [8],[14]C. [6],[13]D. [8],[14],[16]
Find congruent solutions of `155-=7` (mod 4).
Find all congruent solutions of `8x -= 6` (mod 14).
Solve for X, if IX S 1. Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Find the value of m and n. respectively. can be the (f A and B be two sets containing 3 and 6 elements What
Two finite sets have m and n elements. The total number of subsets of first set is 56 more than the total number of subsets of the second set. Find the value of m and n.
Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are. (A) 7, 6 (B) 5, 1 (C) 6, 3 (D) 8, 7
Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The value of m and n isA. 7, 6B. 6, 3C. 5, 1D. 8, 7
If U = {2, 3, 5, 7, 9} is the universal set and A = {3, 7}, B = {2, 5, 7, 9}, then prove that:(i) (A ∪ B)’ = A’ ∩ B’(ii) (A ∩ B)’ = A’ ∪ B’
Let A and B be sets. If A ∩ X = B ∩ X = Φ and A ∪ X = B ∪ X for some set X,show that A = B.(Hints A = A ∩ (A ∪ X), B = B ∩ (B ∪ X) and use distributive law)