Let A 1 2 3 4 5 and B MA NH NV TX AK ME a Define a relatio

Let A = {1, 2, 3, 4, 5} and B = {MA, NH, NV, TX, AK, ME}.

a) Define a relation R from A to B that is a function and contains at least 4 ordered pairs.

b) What is the domain of this function?

c) What is the range of this function?

Please show how you arrived at a) and the domain and range function

Thanks

Solution

a) For a function, there will only be one mapping from A to B for each value of A.The members of B can be repeated in the ordered pairs, but the members of A cannot.
(1,MA)

(2,NH)

(3,AK)

(4,AK)

(5,TX)

All of those are relations of A to B. The easiest way to see if a relation is a function is to check if any values of A are repeated and give a different B value. It\'s absolutely fine for a B value to be repeated (that\'s still a function).

b)

Domain includes all the possible values in A, i.e,

{ 1,2,3,4,5 }

c)

Range includes all values used from B. Here I have used

{ MA , NH , AK , TX }

NOTE

The domain of a function, f, dom(f), is the set {a | ?b s.t. (a, b) ? f}.

The range of f, ran(f), is the set {b | ?a s.t. (a, b) ? f}.