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

Solution :

Given: Set A is a subset of set B and set B is subset of set C.

Let us assume A = {1, 2, 3}; B = {1, 2, 3, 4}; C = {1, 2, 3, 4, 5}

By the definition, subset means all the elements should be present in the parent set.

Here, in the example, we can see that all elements of set A {1, 2, 3} are present in set B {1, 2, 3, 4}

Similarly, every element in set B is in set C.

Another example that we can consider is a set of natural numbers as set A

A set of whole numbers as set B and set of integers as set C.

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

Summary:

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