In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If $A \subset B$ and $x \notin B,$ then $x \notin A$
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If $A \subset B$ and $x \notin B,$ then $x \notin A$
True
Let $A \subset B$ and $x \notin B$
To show: $x \notin A$
If possible, suppose $x \in A$
Then, $x \in B,$ which is a contradiction as $x \notin B$
$\therefore x \notin A$
Similar Questions
Write the following sets in the set-builder form :
$\{ 3,6,9,12\}$
Write the following sets in the set-builder form :
$\{ 3,6,9,12\}$
Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:
$10 \, .........\, A $
Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:
$10 \, .........\, A $
Which of the following are sets ? Justify your answer.
The collection of all boys in your class.
Which of the following are sets ? Justify your answer.
The collection of all boys in your class.
The number of elements in the set $\{x \in R :(|x|-3)|x+4|=6\}$ is equal to
The number of elements in the set $\{x \in R :(|x|-3)|x+4|=6\}$ is equal to
- [JEE MAIN 2021]
Examine whether the following statements are true or false :
$\{ a,b\} \not\subset \{ b,c,a\} $
Examine whether the following statements are true or false :
$\{ a,b\} \not\subset \{ b,c,a\} $