Question

Pas
1. Write the domain and ranges of the following relations. Aslo find their inverse relations
i) R1 = {(1,1),(2,1÷2),(3,1÷3),(4,1÷5)}
ii)R2={(1,1),(4,2),(9,3),(16,4)}
iii) R 3={(1,x),(2,y),(3,z)}
iv) R4 = {(x,y)/y = 2x x,y belongs to N)​

Answer 1

Explanation:

In domain and range of a relation, if R be a relation from set A to set B, then

• The set of all first components of the ordered pairs belonging to R is called the domain of R.

Thus, Dom(R) = {a ∈ A: (a, b) ∈ R for some b ∈ B}.

• The set of all second components of the ordered pairs belonging to R is called the range of R.

Thus, range of R = {b ∈ B: (a, b) ∈R for some a ∈ A}.

Therefore, Domain (R) = {a : (a, b) ∈ R} and Range (R) = {b : (a, b) ∈ R}

Answer 2

Answer:

If R is a relation between set A to set B in the relation's domain and range, then

• The realm of R is the collection of all first parts of ordered pairs that belong to R.

Dom(R) = a A: (a, b) R for the some b B, and so on.

• The range of R is the collection of all second parts of ordered pairs that belong to R.

So, for some a A, the range for R = b B: (a, b) R.

Step-by-step explanation:

As a result, Range (R) = b: (a, b) R and Domain (R) = a: (a, b) R.

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