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About LinkBacksIf R and S are two relations on a set A.
Then which is the correct way to denote the composition of R and S
a) R o S or b) S o R
One author has suggested (a) and the other has suggested (b).
I am confused. Which the correct one. Please reply.
[SOLVED] Composition of two relations
If R and S are two relations on a set A.
Then which is the correct way to denote the composition of R and S
a) R o S or b) S o R
One author has suggested (a) and the other has suggested (b).
I am confused. Which the correct one. Please reply.
Not to be too flippant about, it depends on which author wrote your textbook.Originally Posted by sudeepmansh
Actually, the phrase the composition of R and S is much too vague to really answer that question.
If you know thatthe domains demand that it be written
.
On the other hand, if it werethe vagueness of the phrase would allow for either.
I agree that it is a matter of convention. Whenand
, then the composition of
and
is a subset of
, and
is in the composition if for some
,
and
. So to speak,
However, with all this, we may agree to denote the composition ofor by
. This is just a notation, and as as long as we use it consistently and understand what it means, we can get away with it.
To give an illustration, in Genovia it may be an old tradition to denote 2 to the power 3 as, while the rest of the world writes
. This by itself would not make the collaboration between Genovian and American mathematicians impossible because each of them understands what they are talking about. E.g., Genovians have laws like
, which are exactly the same as in the rest of the world, only written in a weird way.
That said, for functions it is pretty standard to denoteas
. We say "the composition of
and
" because
to remind ourselves about
Now, functions are just special kinds of relations, so to keep the notation consistent, the composition of
TL;DR: read the last paragraph.
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