Let A and B be two non-empty subsets of a set | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given that $A$ is not a subset of $B$ $(A 
ot\subseteq B)$.By definition, this means there exists at least one element $x$ such that $x \in A$ an

Vedclass · Accepted Answer

$A$ and the complement of $B$ are always non-disjoint

Vedclass · Answer

(D) Given that $A$ is not a subset of $B$ $(A 
ot\subseteq B)$.By definition, this means there exists at least one element $x$ such that $x \in A$ and $x 
otin B$.Since $x 
otin B$, it follows that $x \in B^c$ (where $B^c$ is the complement of $B$ with respect to $X$).Therefore, there exists an element $x$ such that $x \in A$ and $x \in B^c$.This implies that the intersection $A \cap B^c$ is non-empty $(A \cap B^c 
eq \emptyset)$.Thus, $A$ and the complement of $B$ are always non-disjoint.

Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then

Similar Questions

The domain of the function $f(x) = \exp (\sqrt {5x - 3 - 2{x^2}} )$ is

The largest possible set of real numbers which can be the domain of $f(x) = \sqrt {1 - \frac{1}{x}} $ is

In a school,$20$ teachers teach either mathematics or physics. If $12$ of them teach mathematics and $4$ teach both subjects,then the number of teachers teaching physics is:

Which of the following sets is infinite?

If $f(x) = 4x^3 + 3x^2 + 3x + 4$,then $x^3 f\left( \frac{1}{x} \right)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module