Question

A subset of a set A is another set that contains only elements from the set A, but may not contain all the elements of A.If B is a subset of A, we write B ⊆ AA proper subset is a subset that is not identical to the original set—it contains fewer elements.If B is a proper subset of A, we write B ⊂ AI can't understand the difference between a subset and a proper subsetI know that a proper subset has fewer elements and is still of the set. does that mean it's just a separate subset and the different symbol is a designation? I'm guessing in connection to other subset? would u clarify please, much appreciated

Answer 1

Here, we want to find the difference a subset and a proper subset

Firstly, we should notice the keyword 'proper' here

Suppose we have three sets A, B and C.

Let us give some values to drive home our point

Let;

A = {1,2,3,4,5}

B = {1,2,3,4,5}

C = {2,3,4}

We can conclude that B is a proper subset of A since all the values we have in B are in A and they have the same number of elements.

But, set C is only a subset of A because although we have all elements of C in A, but both sets do not contain the same number of elements

Symobolical-wise;

We can represent this as;

B ⊂ A while we represent the relationship between A and C as C ⊆ A