Question:

If $A = \{ x : x^2 - 3x + 2 = 0 \}$ , and R is a universal relation on A, then R is

Updated On: Jul 6, 2022
  • $\{(1,1) , (2,2)\}$
  • $\{(1,1)\}$
  • $\{\phi \}$
  • $\{(1,1), (1,2) , (2,1), (2,2)\}$
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The Correct Option is D

Solution and Explanation

$A = \{1,2\}$, as R is universal relation so, $R = A \times A $ R = $\{(1,1), (1,2) , (2,1), (2,2)\}$
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Notes on Relations and functions

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