Consider a 3 functions f, g, h, i. I would like to compose f and g in two different ways such that their domains and ranges are combined using union and intersection.

f: {a,b} -> {c,d}

g: {b,c} -> {d,e}


h = f union g

i = f intersect g

h: {a,b,c} -> {c,d,e}

i: {b} -> {d}

What would be the name of these operators or what is the best way of describing them?

  • $\begingroup$ I can’t tell what you really mean, but the first is probably a piecewise definition and the second a restriction. $\endgroup$
    – Randall
    May 3 at 23:31
  • $\begingroup$ How do you define $f \cup g$ if $f(b) \neq g(b)$? $\endgroup$ May 3 at 23:47
  • $\begingroup$ it does not depend on whether or not f(b) = g(b), I haven't referred to the actual mappings, just the signature $\endgroup$
    – newlogic
    May 3 at 23:53
  • $\begingroup$ It matters because if $f(b) \neq g(b)$ then $f\cup g$ will not be a function. You could define $f \cup g$ as a relation, though. What do you mean by $f \cup g$? $\endgroup$ May 4 at 0:02
  • $\begingroup$ ok sure then yes f union g and f intersect g must both be total functions $\endgroup$
    – newlogic
    May 4 at 0:05


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