math definition of welldefined set Definition of inductive a

Solution

A set S is defined as a well-defined collection of distinct objects, called elements. Here ‘well-defined’ means a unique interpretation i.e. whether any given object is an element of S or it is not an element of S. In other words, a set is said to be well-defined if there is no ambiguity as to whether or not an object belongs to it.

The process of deduction begins with some statements, called \'premises\', which are assumed to be true and it is then required to be determined what else can be true if the premises are true. Deduction can provide absolute proof of the conclusions, if the premises are correct. The premises themselves, however, must be accepted on face value and remain unproven.

The process of induction begins with some data, and then it is determined whether certain general conclusion(s) can logically be derived from this data. In other words, it is determined whether certain theory could explain the data. Although induction does not prove that the theory is correct and often, there are alternative theories that are also supported by the data, but at the same time, in the process of induction, the theory offers a logical explanation of the data.

A universal set is the collection of all objects, including itself, in a particular context and all other sets in that context constitute subsets of the universal set.