Question

Explain the difference between a set that is well defined and one that is not. Give an example of a well-defined set. Name and describe your well-defined set using roster form and set-builder notation. Give an example of at least 1 subset. NO HANDWRITING PLEASE.

Answer 1

A set is the collection of well defined objects or elements which are distinct in that collection. By well defined we mean there should not be any ambiguity while defining the set and its elements. The set is said to be well defined if we can clearly mention its element and identify them without any doubt whether they belong or not belong to the set.

For example if we say that A is a set of good students in a particular class then this will not be a well defined set as goodness of a student is relative and hence is not well defined.

But a set of odd natural numbers(S, say) is a well defined set. Everyone knows the elements of this set and there is no second opinion about the elements of S.

In roster form it can be expressed as, S = {1,3,5,7,9,....}

In set builder method it can be written as, S = {x : x = 2*m-1, m = 1,2,...}

A subset of a set is that set whose all elements belong to the set of which it is a subset.

Let N be a set of all natural numbers then, N = {1,2,3,4,....} and S is a subset of N as all elements of S belong to N.