Functions: Let A = {1, 2, 3, 4} and B = {p, q, r}. Determine

[solomon_13000]

Let A = {1, 2, 3, 4} and B = {p, q, r}. Determine whether the relation R from A to B is a function. If it is a function, give its range.

a) R = {(1, q), (2, r), (3, r), (4, q)}
b) R = {(1, p), (2, q), (3, r), (1, q), (4, p)}
c) R = {(1, r), (2, q), (3, p)}
d) R = {(1, q), (2, q), (3, q), (4, q)}
e) R = {(1, p), (2, q), (3, r), (4, p)}

My solution:

a) Surjective function with a range = q, r
b) Surjective function with a range = p, q, r
c) Injective function with a range = r, q, p
d) not a function
e) Surjective function with a range = p, q, r

Is this correct?

 

[pka]

Re: Functions

Let A = {1, 2, 3, 4} and B = {p, q, r}. Determine whether the relation R from A to B is a function. If it is a function, give its range.
a) R = {(1, q), (2, r), (3, r), (4, q)}
b) R = {(1, p), (2, q), (3, r), (1, q), (4, p)}
c) R = {(1, r), (2, q), (3, p)}
d) R = {(1, q), (2, q), (3, q), (4, q)}
e) R = {(1, p), (2, q), (3, r), (4, p)}

It seems to me judging from the sequence of questions you have posted that you need some real one-on-one tuition. My advise to you is to just stop for a while, spend say two hours and learn all of the definitions involved in your course. Be able to write each of the without having to look at the text. Next go to the text and copy out any worked examples you find there. Copy each three times. These simple if time-consuming acts have done wonders for generations of my students.

For a relation to be a function this must happen: every element in the domain must appear once and only once as a first term of some pair. Now look at part (b), is that true there? Is it true for part (c)? No on both counts. WHY?

For a function to be injective, no two pairs may have the same second term.
In part (e) that is a function which is surjective but not injective. WHY?

Part (d) is most certainly a function with range {q}. It is neither injective nor surjective.

 

[solomon_13000]

I am confuse with

c) R = {(1, r), (2, q), (3, p)}

because each value in the domain is referenced only once by the co domain. So why cant it be a function.

 

[pka]

Where is the 4?
It is once and only once for all of the domain.

Heve you learned the definitions yet.?