Using the fact that a subset of R is closed in R if it conta

Using the fact that a subset of R is closed in R if it contains all of its accumulation points explain why

A. Q is not closed in R
B. N and Z are closed in R

s Usirg fhe fact that a suuct of R is dosed in en costura all f its accunalbron pores Explan

Solution

As the set of real. R contain the set of rational number that is Q is a subset foR . If x belongs to Q then it\'s neighbourhood may contain at least one irrational number but this number belongs to R.hence Q is not closed in R. on the other hand if we take any natural number belongs toN then it\'s neighbourhood contains at least one natural number.Similarly if we take any integer belongs toz then it\'s neighbourhood contain at least one integer soN and Z are closed in R