Question

Let n = 1,2,3, ... ,9. Give examples to illustrate the following facts: a) if A ⊆ B and B ⊆ C, then A ⊆ C?

Answer 1

If A is a subset of B, and B is a subset of C, then A is a subset of C.

Step-by-step explanation:

If A ⊆ B and B ⊆ C, then A ⊆ C. This means that if set A is a subset of set B, and set B is a subset of set C, then set A is also a subset of set C.

For example, let's consider the sets A = {1, 2} , B = {1, 2, 3} , and C = {1, 2, 3, 4}. It can be seen that A is a subset of B (A ⊆ B) since all elements of A are also present in B. Likewise, B is a subset of C (B ⊆ C) since all elements of B are also present in C. Therefore, we can conclude that A is a subset of C (A ⊆ C) because all elements of A are also present in C.