Question

Discuss the following terms giving their definitions and clarifying the definitions by giving suitable examples.

1-subset

2-proper subset

3-improper subset

4-emtpy set

5-power set

can you please write the question using the keypoard to be able to copy and paste the answer not picture . Thanks

Answer 1

Subset : A is a subset of B if and only if every element of A is in B. Example : A = {1, 3, 4} , C= {2, 3, 5} B = {1, 4, 3, 2} => A is a subset of B. But C is not a subset of B as 5 is not present in B.

Proper subset: A is a proper subset of B if and only if every element in A is also in B, and there exists at least one element in B that is not in A.

Example:

{1, 2, 3} is a subset of {1, 2, 3}, but is not a proper subset of {1, 2, 3} but is a improper subset.

{1, 2, 3} is a proper subset of {1, 2, 3, 4} because the element 4 is not in the first set.

Improper subset : The subset consisting of all elements of a given set is called an improper subset

Example:

{1, 2, 3} is a subset of {1, 2, 3}, but is a improper subset of {1, 2, 3}

Empty set: The empty set is a subset of every set, including the empty set itself.

Example: Null set.

Power set: The collection of all subsets of set A is called the power set of A.

For example;

If A = {p, q} then all the subsets of A will be

P(A) = {∅, {p}, {q}, {p, q}}