Prove `sub` is reflexive, antisymmetric and transitive in P(U)

A relation R is defined on the set of natural numbers NN as follows : R {(x,y) : x in NN and x is a multiple of y }. Prove that R is reflexive, antisymmetric and transitive but not symmetric on NN .

Find which two are correct from the following. (i) (x^(3) + sin x) is an odd function. (ii) If A is a set having 4 elements then the power set will have 64 elements. (iii) If a relations is reflexive, antisymmetric and transitive it is called equivalence relation. (iv) The product of two odd functions are even.

Let R be a relation defined by R={(a, b): a >= b, a, b in RR} . The relation R is (a) reflexive, symmetric and transitive (b) reflexive, transitive but not symmetric (c) symmetric, transitive but not reflexive (d) neither transitive nor reflexive but symmetric

Let w denote the words in the english dictionary. Define the relation R by: R = {(x,y) in W xx W | words x and y have at least one letter in common}. Then R is: (1) reflexive, symmetric and not transitive (2) reflexive, symmetric and transitive (3) reflexive, not symmetric and transitive (4) not reflexive, symmetric and transitive

Let w denote the words in the english dictionary. Define the relation R by: R = {(x,y) in W xx W | words x and y have at least one letter in common}. Then R is: (1) reflexive, symmetric and not transitive (2) reflexive, symmetric and transitive (3) reflexive, not symmetric and transitive (4) not reflexive, symmetric and transitive

Let w denote the words in the english dictionary. Define the relation R by: R = {(x,y) in W xx W | words x and y have at least one letter in common}. Then R is: (1) reflexive, symmetric and not transitive (2) reflexive, symmetric and transitive (3) reflexive, not symmetric and transitive (4) not reflexive, symmetric and transitive

Let R be a relation defined by R={(a,b):a>=b,a,b in R}. The relation R is (a) reflexive,symmetric and transitive (b) reflexive,transitive but not symmetric ( d) symmetric,transitive but not reflexive (d) neither transitive nor reflexive but symmetric

Let A={1, 2, 3) be a given set. Define a relation on A swhich is (i) reflexive and transitive but not symmetric on A (ii) reflexive and symmeetric but not transitive on A (iii) transitive and symmetric but not reflexive on A (iv) reflexive but neither symmetric nor transitive on A (v) symmetric but neither reflexive nor transitive on A (vi) transitive but neither reflexive nor symmetric on A (vii) neither reflexive nor symmetric and transitive on A (vii) an equivalence relation on A (ix) neither symmetric nor anti symmmetric on A (x) symmetric but not anti symmetric on A

In a set of real numbers a relation R is defined as xRy such that |x|+|y|lt=1 (A)then relation R is reflexive and symmetric but not transitive (B)symmetric but not transitive and reflexive (C)transitive but not symmetric and reflexive (D) none of reflexive, symmetric and transitive

(n)/(m) means that n is a factor of m,then the relation T' is (a) reflexive and symmetric (b) transitive and reflexive and symmetric (b) and symmetric (d) reflexive,transtive and not symmetric