Question

Use a venn diagram to illustrate the relationships \(A \subset B\)and \(B \subset C\).

Short answer

\(A \subset B\) and \(B \subset C\)is illustrated using Venn diagram.

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:

\(A \subset B\) and \(B \subset C\)

To illustrate the relationships \(A \subset B\) and \(A \subset C\)

There are two cases:

Case 1:C is a subset of B.

\(C \subset B\)

The venn diagram of A should be completely within the venn diagram of C since A is a subset of C.

The venn diagram of C should be completely within the venn diagram of B since C is a subset of B.

Case 2:B is a subset of C.

\(B \subset C\)

The venn diagram of A should be completely within the venn diagram of B since A is a subset of B.

The venn diagram of B should be completely within the venn diagram of C since B is a subset of C.

Now, the overall venn diagram for \(A \subset B\) and \(B \subset C\)is:

Thus, \(A \subset B\) and \(B \subset C\) is illustrated using Venn diagram.