Discrete mathematics function relation question. I justcan not understand how partial functio works. for example, I thinka) is not
total function, because y+5=3x is not always true forevery 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 therelation is a function, only a partial function, or not even apartial function.
If it’s a (total) function, write “total function”, and providea proof that it meets both requirements.
If it’s partial but not total, write “partial, but not totalfunction”, provide a proof that it meets the second requirement(uniqueness), and provide a counterexample to prove that it doesnot meet the first requirement (existence).
If it’s not even a partial function, write “not a partialfunction”, and give a counterexample to prove that it doesn’t meetthe 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}.
