1

I was doing chapter on relation and came up on the topic "types of relation", i studied about void and universal relation and then there was witten that "Both void and universal relation are sometimes called trivial relation." What does trivial relation mean? Explain!

It is from RD sharma class 12th Book.

Krishna
  • 27
  • 1
    The word 'trivial' means especially simple. –  May 24 '21 at 17:23
  • 1
    void = empty. trivial = obvious. – David P May 24 '21 at 17:37
  • 1
    "trivial" usually means when only the must basic and fundamental requirements for a definition are meant. This often means means if it's possible to have no elements or conditions the trivial case wont have any elements or conditions. A relation on $A$ is a subset of $A\times A$ contain some collection of ordered pairs. So a trivial relation would be the minimal collection of ordered pairs... namely no actual pairs... i.e the empty set.... a relation where nothing is related to anything. – fleablood May 24 '21 at 18:02

1 Answers1

3

The word trivial is used in cases where the object meets the definition of the thing being talked about but is neither the motivating factor nor a particularly important example.

If, for example, we define a binary relation between two sets $A$ and $B$ to be a subset of $A\times B$ it is immediately true that both the empty set and the entire set $A\times B$ are binary relations because they are subsets of $A\times B$. But that definition is really meant to capture a relation as an association between elements of $A$ and elements of $B$. Hence, we call those examples trivial.

John Douma
  • 11,426
  • 2
  • 23
  • 24