Let W denote the words in the English dictionary. Define the relation R by: R = (x,y), ∈ W × W: the words x and y have at least one letter in commona Then R is

Question

Let W denote the words in the English dictionary. Define the relation R by: R = (x,y), ∈ W × W: the words x and y have at least one letter in commona Then R is (A) reflexive, not symmetric and transitive (B) not reflexive, symmetric and transitive (C) reflexive, symmetric and not transitive (D) reflexive, symmetric and transitive

Tardigrade Admin · Accepted Answer

Let w ∈ W then (w, w) ∈ : R : ∴ : R is reflexive. Also if w1, w2 ∈ W and (w1,w2) ∈ R, then (w2, w1) ∈ R. ∴ R is symmetric. Again Let w1 = I N K, w2 = L I N K, w3 = L E T Then (w1, w2) ∈ R [∵ I, N are the common elements of w1, w2](w2,w3)∈ R [∵ L is the common element of w2, w3] But (w1, w3) ∉ R [∵ there is no common element of w1,, w3] ∴ R is not transitive.

Q. Let W denote the words in the English dictionary. Define the relation R by : R={(x,y),∈W×W : the words x and y have at least one letter in commona} Then R is

reflexive, not symmetric and transitive

not reflexive, symmetric and transitive

reflexive, symmetric and not transitive

reflexive, symmetric and transitive

Q. Let W denote the words in the English dictionary. Define the relation $R$ by : $R = {(x, y), \in W \times W$ : the words $x$ and $y$ have at least one letter in commona $}$ Then R is