Question

Let A=\left\\{ \left\\{ 1,2,3 \right\\},\left\\{ 4,5 \right\\},\left\\{ 6,7,8 \right\\} \right\\} . Verify whether the following statement is true or false. Why?
(i) $\varphi \in A$

Answer 1

Hint:The symbol ‘ $\in$ ‘ is an element of or belongs to which symbolizes set membership,, first assess the statement by comparing the elements with the given set A and then write true/ false.

Complete step-by-step answer:
In the question we are given a set A such that it represents as \left\\{ 1,2,3 \right\\},\left\\{ 4,5 \right\\},\left\\{ 6,7,8 \right\\}. Further a statement is written that $\varphi \in A$ and we have to say that it is true or false.
At first, we briefly understand what is set.
In mathematics sets is a well defined collection of distinct objects, considered as an object in its own right. The arrangement of the objects in the set does not matter. For example, the number 2,4,6 are distinct and considered separately, but they are considered collectively. Then form a single set of size three written as \left\\{ 2,4,6 \right\\} which could also be written as \left\\{ 2,6,4 \right\\} .
There are various symbols used in sets and each has a different meaning. Here, in the statement a symbol ‘ $\in$ ' is given. This symbol’s name is an element of or belongs to which symbolizes set membership, for example if C=\left\\{ 1,2,3 \right\\} then we can say $1\in C$ .
In ‘A’ elements are \left\\{ 1,2,3 \right\\},\left\\{ 4,5 \right\\} and \left\\{ 6,7,8 \right\\} but in the question it is asked whether $\varphi \in A$ is true or false. As we see $\varphi$ is not an element of A.
So, the statement is false.

Note: Students generally have confusion between this symbol as they are so much used in the sets just like confusion between $\in$ and C, where former represent set membership and latter one represent one is a subset of another.