Q.8
x y 0 0 0
If pq R = 0 0 0 , then the order of R is
u v 0 0 i

(A) 2 · 3
(B) 3 · 2
(C) 2 2
(D) 3 · 3

Answer:
The relation $R$ has order $3\times 2$ (option B).

Interpreting the Question

The given matrix of relation $R$ is shown with rows labelled by elements $p,q,u$ and columns labelled by elements $x,y$.
So:

• Row set (domain of relation) = $\{p,q,u\}$ → 3 elements

• Column set (codomain of relation) = $\{x,y\}$ → 2 elements

The order of a relation matrix is always:

$$\text{(number of rows)}\times \text{(number of columns)}$$

Hence the order of $R$ is $3\times 2$.

Why Option B (3×2) Is Correct

• The matrix shows three distinct row labels: $p,q,u$.

• The matrix shows two distinct column labels: $x,y$.

• Therefore, there are 3 rows and 2 columns, so the matrix (and the relation) has order $3\times 2$.

This matches option (B) 3·2, so option B is correct.

Why the Other Options Are Wrong

Option (A) 2·3

• This would mean 2 rows and 3 columns.

• But the matrix clearly has 3 row labels ($p,q,u$) and only 2 column labels ($x,y$), so 2×3 does not match the given structure.

Option (C) 2 2 (i.e., 2×2)

• A 2×2 matrix would have only 2 rows and 2 columns.

• Here, there are 3 row labels, not 2, so the order cannot be 2×2.

Option (D) 3·3

• A 3×3 matrix would require 3 rows and 3 columns.

• The relation matrix has only 2 column labels ($x,y$), so 3×3 is impossible for this question.

Short Concept Recap for SEO

In matrix representation of a relation, order of a relation from matrix means the size of the matrix: number of elements in the domain (rows) multiplied by the number of elements in the codomain (columns).
In this problem, 3 elements in the row set and 2 in the column set give an order of $3\times 2$, so the correct option is (B) 3·2.