Question

Find the two sets A and B such that\(A \in B\)and\(A \subseteq B\).

Short answer

\(a = \left\{ {} \right\}\) and .\(b = \left\{ {\left\{ {} \right\}\left\{ {1,2} \right\}} \right\}\).

Step-by-step solution

Given Data:

If every element of X is also an element of Y, then X is a subset of Y considering X and Y are not the same set.

It is given that:

\(A \in B\)and \(A \subseteq B\).

To determine the two sets A and B such that \(A \in B\)and\(A \subseteq B\)

Consider the two sets:

Set \(a = \left\{ {} \right\}\) and \(b = \left\{ {\left\{ {} \right\}\left\{ {1,2} \right\}} \right\}\)

Now, from above sets, it can be noted that \(a\) belongs to set \(b\) as the empty set is a subset of every set.

Therefore, it is written as \(A \in B\).

By the definition of subset, it is clear that every element of set A should be contained in set B.

Therefore, it is written as \(A \subseteq B\).

Thus, the two sets are \(a = \left\{ {} \right\}\) and \(b = \left\{ {\left\{ {} \right\}\left\{ {1,2} \right\}} \right\}\).