Find the subset of set A={p,q,r,s,t}

did you mean, find the number of subsets ?

if so, there would be 2^5 or 32 of them, including the null set and the entire set

Please give answer

To find subsets of a set, we can use the power set concept. The power set of a set A is the set of all possible subsets of A, including the empty set and the set itself.

In this case, the set A = {p, q, r, s, t}.

To find the subsets of A, we can follow these steps:

Step 1: Determine the total number of elements in the set A.

In this case, the set A has 5 elements: p, q, r, s, and t.

Step 2: Calculate the total number of subsets.
The number of subsets of a set with n elements is given by 2^n.

In this case, n = 5, so the total number of subsets is 2^5 = 32.

Step 3: List all possible subsets.

Here are all the possible subsets of set A:

Subsets with 0 elements: {}

Subsets with 1 element: {p}, {q}, {r}, {s}, {t}

Subsets with 2 elements: {p, q}, {p, r}, {p, s}, {p, t}, {q, r}, {q, s}, {q, t}, {r, s}, {r, t}, {s, t}

Subsets with 3 elements: {p, q, r}, {p, q, s}, {p, q, t}, {p, r, s}, {p, r, t}, {p, s, t}, {q, r, s}, {q, r, t}, {q, s, t}, {r, s, t}

Subsets with 4 elements: {p, q, r, s}, {p, q, r, t}, {p, q, s, t}, {p, r, s, t}, {q, r, s, t}

Subsets with 5 elements: {p, q, r, s, t}

So, the subset of set A = {p, q, r, s, t} is:

{}, {p}, {q}, {r}, {s}, {t}, {p, q}, {p, r}, {p, s}, {p, t}, {q, r}, {q, s}, {q, t}, {r, s}, {r, t}, {s, t}, {p, q, r}, {p, q, s}, {p, q, t}, {p, r, s}, {p, r, t}, {p, s, t}, {q, r, s}, {q, r, t}, {q, s, t}, {r, s, t}, {p, q, r, s}, {p, q, r, t}, {p, q, s, t}, {p, r, s, t}, {q, r, s, t}, {p, q, r, s, t}

To find the subsets of a set, you need to consider all possible combinations of its elements. In this case, the set A has five elements: p, q, r, s, and t. To find all possible subsets, you need to consider the options of including or excluding each element.

Here are all the possible subsets of set A:

1. Empty Set (∅): This is the subset that contains no elements.
2. Subset with one element: This includes subsets containing each individual element of set A. For example, {p}, {q}, {r}, {s}, and {t}.
3. Subset with two elements: This includes subsets containing any pair of elements from set A. For example, {p, q}, {p, r}, {p, s}, {p, t}, {q, r}, {q, s}, {q, t}, {r, s}, {r, t}, {s, t}.
4. Subset with three elements: This includes subsets containing any three elements from set A. For example, {p, q, r}, {p, q, s}, {p, q, t}, {p, r, s}, {p, r, t}, {p, s, t}, {q, r, s}, {q, r, t}, {q, s, t}, {r, s, t}.
5. Subset with four elements: This includes subsets containing any four elements from set A. For example, {p, q, r, s}, {p, q, r, t}, {p, q, s, t}, {p, r, s, t}, {q, r, s, t}.
6. Subset with all five elements: This is the subset which contains all the elements of set A. In this case, it is {p, q, r, s, t}.

Therefore, the subsets of set A are:
{∅, {p}, {q}, {r}, {s}, {t}, {p, q}, {p, r}, {p, s}, {p, t}, {q, r}, {q, s}, {q, t}, {r, s}, {r, t}, {s, t}, {p, q, r}, {p, q, s}, {p, q, t}, {p, r, s}, {p, r, t}, {p, s, t}, {q, r, s}, {q, r, t}, {q, s, t}, {r, s, t}, {p, q, r, s}, {p, q, r, t}, {p, q, s, t}, {p, r, s, t}, {q, r, s, t}, {p, q, r, s, t}}.