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 $x \in A$ and $A \in B,$ then $x \in B$
False
Let $A=\{1,2\}$ and $B=\{1,\{1,2\},\{3\}\}$
Now, $2 \in\{1,2\}$ and $\{1,2\}$ $\in\{\{3\}, 1,\{1,2\}\}$
$\therefore A \in B$
Howerer, $2 \notin\{\{3\}, 1,\{1,2\}\}$
Which of the following are examples of the null set
$\{ y:y$ is a point common to any two parallellines $\} $
List all the elements of the following sers :
$D = \{ x:x$ is a letter in the word $"\mathrm{LOYAL}" $ $\} $
Examine whether the following statements are true or false :
$\{ a,e\} \subset \{ x:x$ is a vowelin the English alphabet $\} $
The number of elements in the set $\{x \in R :(|x|-3)|x+4|=6\}$ is equal to
Which of the following are sets ? Justify your answer.
The collection of all even integers.