Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective: `{(x ,\ y): x` is a person, `y` is the mother of `x}` (ii) `{(a ,\ b): a` is a person, `b` is an ancestor of `a}`

Explanation

(i) We have,`{(x,y):x`is a person, `y` is the mother of `x``}`

Clearly each person `x` has only one biological mother.

So above set of ordered pair is a function.

Now more than one person may have same mother.

So, function is many-one and surjective.

(ii)We have `{(a,b):` a person, `b` is an ancestor of `a``}`
Clearly any person a has more than one ancestors.
So, it does not represent function.