Let A be the set of people, and P, F, M, S, B the relations over A of ‘parent of’, ‘father of’, ‘mother of’, ‘sister of’ and ‘brother of’, respectively. Describe the SºP relation in real world?
Solution in the book.
SºP D ‘parent of a sister of’. Reason: a is a parent of a sister of c iff there is an x such that a is a parent of x and x is a sister of c.
My logic.
If aSb then a is the sister of b. If cPd then c is the parent of d.|=> uSºPv would mean that there exists "x" such that uSxPv, which in turn would mean that "u" is the sister of "x" and "x" is the parent of v. So if we draw this. It would look like this.
u-----x
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v
So the relation of u to v is "sibling's child". (We don't know if x is a man or woman).
I would appreciate if someone could explain the solution and show the fallacy in my logic.