Question:

Let $A = \{a_1, a_2\}$ and $B = \{b_1, b_2\}$, then the number of relations from $A$ to $B$ is

Updated On: Jul 6, 2022
  • $4$
  • $8$
  • $16$
  • $2$
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The Correct Option is C

Solution and Explanation

$n\left(A\right) = 2, n\left(B\right) = 2$ $\Rightarrow n\left(A \times B\right) = 4$ $\therefore$ Number of relations $=2^{n\left(A \times B\right)}$ $=2^4=16$
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Concepts Used:

Relations and functions

A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.

A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.

Representation of Relation and Function

Relations and functions can be represented in different forms such as arrow representation, algebraic form, set-builder form, graphically, roster form, and tabular form. Define a function f: A = {1, 2, 3} → B = {1, 4, 9} such that f(1) = 1, f(2) = 4, f(3) = 9. Now, represent this function in different forms.

  1. Set-builder form - {(x, y): f(x) = y2, x ∈ A, y ∈ B}
  2. Roster form - {(1, 1), (2, 4), (3, 9)}
  3. Arrow Representation