Question

Discrete mathematics function relation question. I just can not understand how partial functio works. for example, I think a) is not

total function, because y+5=3x is not always true for every domain. However, I do not know it is just partial function, but I do not know how to explain it.

For each of the following relations, determine whether the relation is a function, only a partial function, or not even a partial function.

If it’s a (total) function, write “total function”, and provide a proof that it meets both requirements.

If it’s partial but not total, write “partial, but not total function”, provide a proof that it meets the second requirement (uniqueness), and provide a counterexample to prove that it does not meet the first requirement (existence).

If it’s not even a partial function, write “not a partial function”, and give a counterexample to prove that it doesn’t meet the second requirement (uniqueness).

(a) The relation L on R defined by L = {(x, y) | y + 5 = 3x}.

(b) The relation P1 from Z to Z defined by P1 = {(x, y) | x · y = 6}.

(c) The relation P2 from R ∗ to R ∗ defined by P2 = {(x, y) | x · y = 6}. R ∗ is the set of all non-zero real numbers.

(d) The relation E on the set of all strings defined by L = {(s, t)| the length of s = the length of t}.

Answer 1