Question

In the first part of this question, suppose that the universal set, i.e., the set of all elements we consider, is given by S = {n ∈ Z:0 ≤ n<100). Moreover, let P be the set of prime numbers in S, let E be the set of even numbers in S, and let F = {1,2,3,5,8, 13, 21, 34, 55, 89). (i) Describe the following sets either by listing all of their elements or precisely char- acterising them in words. (a) Eᶜ

Answer 1

The set Eᶜ is the complement of the set of even numbers in the universal set S. It consists of all the odd numbers in S. E within the universal set S, which includes all integers.

Step-by-step explanation:

The set Eᶜ is the complement of the set E. The complement of a set consists of all elements that are not in the original set. Given that E is the set of even numbers in the universal set S, Eᶜ would be the set of all elements in S that are not even numbers.

In the first part of this question, Ec represents the complement of the set of even numbers E within the universal set S, which includes all integers from 0 to 99. To find Ec, we list all the numbers in S that are not even, which means we are looking for all the odd numbers in the range. Therefore, Ec consists of all odd numbers from 1 to 99.

In this case, the universal set S is defined as {n ∈ Z: 0 ≤ n < 100}. Therefore, Eᶜ would consist of all the odd numbers in S. We can represent Eᶜ as a set by listing its elements:

Eᶜ = {1, 3, 5, 7, 9, ..., 99}