Let g = {−2, 0, 2} and h = {4, 6, 8} and define a relation v from g to h as follows: for every (x, y) is in g ✕ h, (x, y) is in v means that x − y 4 is an integer. (a) is 2 v 6? yes no is −2 v 8? yes no is (0, 6) is in v? yes no is (2, 4) is in v? yes no (b) write v as a set of ordered pairs. (enter your answer in roster notation.) (c) write the domain set of v. (enter your answer in roster notation.) write the co-domain set of v. (enter your answer in roster notation.)

a) Yes, No, No No

b) V={(-2,6),(0,4),(0,8),(2,6)}.

c) Domain={-2,0,2}

d) Co-domain={4,6,8}

Step-by-step explanation:

If A and B are two sets then the cartesian product of A and B denoted by is the set of all ordered pairs (a,b), where and

={}

The given relation is

for every (x, y) is in G ✕ H, (x, y) is in V means that is an integer

a) Yes, since -1 is an integer

b) No, since -2.5 is not an integer

c) No, since -1.5 is not an integer

No, since -0.5 is not an integer

G ✕ H={(-2,4),(-2,6),(-2,8),(0,4),(0,6),(0,8),(2,4),(2,6),(2,8)}

From this set, we have some ordered pairs that satisfy the definition of V.

V={(-2,6),(0,4),(0,8),(2,6)}.....The difference of these ordered pairs are multiples of 4.

c) The domain of V is the set of the first coordinates of the ordered pairs of V

Domain={-2,0,2}

The co domain of v is the set of all the second coordinates of the ordered pairs of V

Co-domain={4,6,8}

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