Explain why the four sets are true based on the above inform

Explain why the four sets are true based on the above information.

Example 1.2.1. (i) There are many acceptable ways to assert the contents of a set. In the previous section, the set of natural numbers was defined by listing the elements: N={1,2,3,...}. (ii) Sets can also be described in words. For instance, we can define the set E to be the collection of even natural numbers. (iii) Sometimes it is more efficient to provide a kind of rule or algorithm for determining the elements of a set. As an example, let S = {r E Q : r^2 = 2. Using the previously defined sets to illustrate the operations of intersection and union, we observe that N U E = N, N n E = E, N n S = {1}, and E n S = 0.

Solution

N U E = N , since E is subset of N ,so all the eloements of E are in N and remaining odd elements

hence the result

similalry N intersection E = E

since E is set of evven numbers and all the even numbers are in N

N intersection S = {1} since 1 is the only natural number as n^2<2

E intersection S = null

since E is set of even numbers so , E starts from 2

but the only natural number in S is 1

hence null