Please 3&4&5 3. Let S = {1,2,...,7,8) be ordered as in figure below. Consider the subset...

(3) We have given:

(a)

Since every number in A is less than or equal to 7, so 7 is upper bound of A.

Therefore, every number in S greater than or equal to 7 is upper bound for A.

Set of upper bounds of A = {7, 8}

(b)

Similarly every number in A is greater than or equal to 3, so 3 is lower bound of A.

Therefore, every number in S leass than or equal to 3 is lower bound of A.

Set of lower bounds of A = {1, 2, 3}

(c) least upper bound of A is called as supremum of A.

Here least upper bound of A is 7.

Therefore, sup(A) = 7.

(d) greatest lower bound is called infimum of A.

Here greatest lower bound of A is 3.

Therefore, inf(A) = 3.