Notation of Elements of a Set

Q. Which of the following is correct notation?

1. $\in \to$ there exist
2. $\forall \to$ for all
3. $\exists \to$ such that
4. $:\to$ belongs to

Q. Which of the following is correct notation?

1. $\in \to$ there exist
2. $\forall \to$ for all
3. $\exists \to$ such that
4. $:\to$ belongs to

Q. If $\varphi$ denotes the empty set, then which of the folowing is correct

1. $\varphi \in \varphi$
2. $\varphi \in \left\{\varphi \right\}$
3. $\left\{\varphi \right\}\in \left\{\varphi \right\}$
4. $0\in \varphi$

Q. If "$x$" is an element of the set "$Y$", then we write it as

1. $x\in Y$
2. $Y\in x$
3. $x\notin Y$

Q. If $a$ is an element "not in" set $A$, then $a\notin A.$

1. No
2. Yes

Q. Set $Y$ is a set of all the letters in the word $CRICKET,$ then select the correct option(s).

1. $I\in Y$
2. $C\notin Y$
3. $A\in Y$
4. $Z\notin Y$