Question

38.
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 atleast 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​

Answer 1

Step-by-step explanation:

Define the relation R by: R = {(x,y)∈W×W | words x and y have at least one letter in common}. ... ∴ (x,x) has every letter common, therefore R is reflexive. Let (x,y)∈R then (y,x)∈R as y and x have at least one letter in common, this implies, R is symmetric.

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