Question

Which of the following is the universal quantifier?
1) $ \in $
2) $ \subset $
3) $\forall $
4) $\exists $

Answer 1

Hint:
We know that a universal quantifier means a logical equivalent to ‘for all’, hence we will go through each of the given options and after studying them, we will mark the most suitable one to get the answer.

Complete step by step solution:
A universal quantifier means a logical equivalent to ‘for all’, hence we need to find a symbol that is logically equivalent to ‘for all’.
According to the question,
Option 1: $ \in $
The $ \in $ represents a logically equivalent statement of ‘belongs to’, if an element ‘a’ belongs to a set ‘A’, then we can write it as
$ \Rightarrow a \in A$
But it is not equivalent to a universal quantifier, hence this is not the correct option
Option 2: $ \subset $
The $ \subset $ represents a logically equivalent statement of ‘subset’, if all the elements of a set ‘a’ belong to a set ‘A’, then we can write it as
$ \Rightarrow a \subset A$
But it is not equivalent to a universal quantifier, hence this is not the correct option
Option 3: $\forall $
The $\forall $ represents a logically equivalent statement of ‘for all’, if we need to address a whole set or a whole group, $\forall $ is used. If we need to address all the elements of a set a, we will use
$ \Rightarrow \forall a$
Since it is equivalent to a universal quantifier, hence this is the correct option
Option 4: $\exists $
The $\exists $ represents a logically equivalent statement of ‘there exists’, if an element ‘a’ exists in a set ‘A’, then $\exists $ is used to tell this
$ \Rightarrow a\exists A$
But it is not equivalent to a universal quantifier, hence this is not the correct option

Hence, the final answer is C.

Note:
These questions are direct knowledge-based, if we don't know the theory, we have no chance to solve this question with logical explanations, that is why theory is also an important part of Maths.