Find and if for every positive integer i Ai i i l i 2 Ai

Find and if for every positive integer i, Ai- = {i, i + l, i + 2, ...}. Ai = {0, i}, Ai = (0, i), that is, the set of real numbers x with 0 Ai, = (i, infinity), that is, the set of real numbers x with x > i.

Solution

a) Ai = { i, i+1, i+2, i+3 }

UAi = List of all the natural numbers starting from 1 to infinite

(Intersection)Ai = Phi, hence there is no common element between the sets

b) Ai = {0,i}

UAi = List of all the whole numbers starting from 0 to infinite

(Interesection)Ai = 0, it will contain the only zero element which is common to all the sets

c) Ai = (0,i)

UAi = List of the real numbers in the range of (0,infinite)

(Intersection)Ai = it will be a null subset

d) Ai = (i,infinite)

UAi = list of the real numbers in the range of (0,infinite)

Intersection Ai = it will be null set (phi element)