There are subsets a {1,2,3} and B {1,2,3,4}. Is a a subset of B or a proper subset?

There are subsets a {1,2,3} and B {1,2,3,4}. Is a a subset of B or a proper subset?

It should be called set a {1,2,3} set B {1,2,3,4}, not a subset!
For two sets u and a, if any element of set a is an element of set u, we say that set a is contained in set u, or set u contains set a, that is to say, set a is a subset of set U
If B is a subset of u and at least one element of u does not belong to B, then set B is called the proper subset of set U
U. A and B are three sets. For example: u = {1,2,3}; a = {1,2,3}; b = {1,2}
Do you understand? Let's make clear the definition of the two first!

Let u = {1.2.3.4.5.6.7.8.9}, a = {1.2.3} and B = {4.5.6}. Find the number of nonempty proper subsets of A

The nonempty proper subsets of a are as follows:
{1},{2},{3}
{1,2},{1,3},{2,3}
{1,2,3}
There are seven

If {1,3} is a proper subset of a and a is a subset of {1,3,5,7,9}, what is the number of sets a

5