Consider the relation R = {(2x,x2) : x 2 Z} on Z. (1) Is 6R9? (2) Does 1 belong to the domain of the relation R? (3) Is the relation R a function from Z into Z? Explain.

1) yes 6 R 9

2) 1 is not a member of the domain

3) Yes because R is a subset of Z x Z

can you show me any work to find your answers?

Do you mean an explanation of the answers

yes

1) Put x =3 (Which we can do since 3 is a member of Z) and we get (6,9) as a member of the Relation R

2) To get 1 as a member of R we must put in x = 1/2 the domain we have and 1/2 is not a member of Z

2) To get 1 as a member of R we must put in x = 1/2

but 1/2 is not a member of Z

3) the relation is actually (0.0), (2,1), (4,4), (6,9) (8,16)....... and (-2,1), (-4, 4) (-6,9), (-8,16),,,,,

so this is a subset of ZXZ

Sorry I did not read the Q properly

Although it is a relation it is not a function because all the odd nimber have no partners

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