Question:

Let A = { $(x,y): y = e^{-x}$ } and B = { $(x,y):y=-x$ }. Then the correct statement is :

Updated On: Aug 21, 2023

$A \cap B = \phi$
$A \subset B$
$B \subset A$
$A \cup B = \{(01),(0,0)\}$

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The Correct Option is A

Solution and Explanation

The correct option is(A): A∩B=ϕ

given that : y=e^x and y= e^-x

= e^x=e^-x or e^2x=1

Then x=0, hence y=1

therefore; the curve meet at(0,1) so that

A∩B=(0,1), OR A∩B=ϕ.

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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.

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

Let A = { (x,y):y=e−x (x,y): y = e^{-x} (x,y):y=e−x } and B = { (x,y):y=−x (x,y):y=-x (x,y):y=−x }. Then the correct statement is :