Question:

The cartesian product A×A A\times A has 99 elements among which are found (−1,0) (-1,0) and (0,1), (0,1), then set AA = ?

Updated On: Jun 23, 2024
  • {1,  0} \{1,\,\,0\}
  • {1,  −1,   0} \{1,\,\,-1,\,\,\,0\}
  • { 0,  −1} \{\,0,\,\,-1\}
  • {1,  −1} \{1,\,\,-1\}
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is B

Solution and Explanation

Given, n(A×A)=9       ⇒     n(A)×n(A)=9 n(A\times A)=9\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,n(A)\times n(A)=9 which is possible when, n(A)=3. n(A)=3. i.e., set A contain only three elements i.e., A={1,−1,0} A=\{1,-1,0\} So, A×A A\times A contain (−1,0) (-1,0) and (0, 1) (0,\,1)
Was this answer helpful?
0
0

Top Questions on Relations and functions

View More Questions

Questions Asked in JKCET exam

View More Questions

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