Q Function Types I had submitted it before but Im not so sur

Q Function Types

I had submitted it before, but I\'m not so sure the answear I got was right.

Solution

Here rule is that for a relation ,being a function, its each element of domain should be associated with a unique element in its codomain. But we observe in case a) that we have two ordered pair (1,a) and (2,a) in which two elements of domain are associated with one element of codomain.

So it is cleared that it is not injecttive (1-1) and hence not bijective. Further it is also not surjective as element d is not associated with any of its preimage.

So P is neither surjective, nor injective , nor bijective.

===============================================================================

Now in function Q, we find two pairs (1,c) and (4,c) that show that two elements of domain are associted with one same element of codomain that means it is not injective and thus it is not bijecttive also, but as all four elements a,b,c and d of its codomain are associated with its preimage, so it is surely surjective.

So Q is partially surjective.

=================================================================================

In function R, we find that each element of domain is associated with only one unique element of codomain, as well as each element of codomain is associated with an element of preimage, that means it is injective, surjective and hence bijective also.