PUMPA - SMART LEARNING

மதிப்பெண்கள் எடுப்பது கடினமா? எங்கள் AI enabled learning system மூலம் நீங்கள் முதலிடம் பெற பயிற்சியளிக்க முடியும்!

டவுன்லோடு செய்யுங்கள்We acquired an elaborated idea of sets, domain, range and other fundamental concepts. Keeping all this in mind, try to answer this question.

If you're answer is

**Should all sets have a relationship?**If you're answer is

**No**, you're absolutely correct. Some sets have no relation and are referred to as empty sets or null sets.Null relation:

When there is no relation between any set elements, that relation is called a null set or an empty set.

Example:

If set \(A\) denotes the states of India and \(B\) denotes the capital of the Indian states.

That is \(A = \{Kerala, Gujarat, Punjab\}\) and \(B = \{Chennai, Mumbai, Kolkata\}\).

We can notice here, the set \(A\) and \(B\) (states and capital) contain no relation \(R\).

Thus \(R\) contains no element. Therefore, a relation which contains no element is called a “null relation”.

A null relation is denoted by $\varnothing $. Here, \(R =\) $\varnothing $. Similarly, an empty set is represented by \(\{\}\). Here, \(R = \{\}\)

Total number of relations

**Do you know how to find the total number of relations?**Now we will learn how to calculate it.

If the number of elements in the set \(A\) \(= n(A)\) \(= m\) , then the number of elements in the set \(B\) is \(=n (B)\) \(= n\), then the total number of relations that exist from \(A\) to \(B\) is \(2^m\)\(^n\).

Example:

Let the two sets \(A = \{(4, 8, 13\}\) and \(B = \{(15, 11\}\).

Here, \(n (A) = 3\) and \(n (B) = 2\).

**Therefore**,

**the total number of relations that exist from**\(A\) to \(B\)

**is**${2}^{3\times 2}={2}^{6}$.

**Now we will practice some exercises based on the concepts we discussed**.