find the power set of the following set
A = (prime factors of 210)
can you explain how 2,3,5,7
are prime factor of 210
lets look at the prime factors of 210
2,3,5,7
So there must be 2^4 members of the power set, or 16 elements, including the empty set.
Power set: 2, 3, 5, 7, (2,3), (2,5), (2,7), (3,5), (3,7), (5,7), (2,3,5), (2,3,7), (2,5,7), (3,5,7), (2,3,5,7), (empty set)
Check that. Are there more?
To find the power set of a set, we need to list all possible subsets of the set, including the empty set and the set itself.
To find the prime factors of 210, we can start by finding the prime numbers that divide 210.
The prime factors of 210 are:
2, 3, 5, 7
Now, let's find the power set of A = {2, 3, 5, 7}.
Step 1: Write down all the individual elements:
{}, {2}, {3}, {5}, {7}
Step 2: Write down all possible combinations of two elements:
{2,3}, {2,5}, {2,7}
{3,5}, {3,7}
{5,7}
Step 3: Write down all possible combinations of three elements:
{2,3,5}, {2,3,7}
{2,5,7}
{3,5,7}
Step 4: Write down the combination of all elements:
{2,3,5,7}
Step 5: Finally, include the empty set {}.
The power set of A = {2, 3, 5, 7} is:
{ {}, {2}, {3}, {5}, {7}, {2,3}, {2,5}, {2,7}, {3,5}, {3,7}, {5,7}, {2,3,5}, {2,3,7}, {2,5,7}, {3,5,7}, {2,3,5,7} }
So, the power set of A is a set of 16 subsets.
To find the power set of a set, we need to consider all the possible subsets of that set, including the empty set and the set itself.
Step 1: Find the prime factors of 210.
To find the prime factors of 210, we can use prime factorization method:
210 = 2 × 3 × 5 × 7
Step 2: Write down all the subsets of the set of prime factors.
The set of prime factors of 210 is {2, 3, 5, 7}. We can write down all the subsets using a systematic approach.
- Start with the empty set: {}
- Add the first element: {2}
- Add the second element: {3}
- Add the third element: {5}
- Add the fourth element: {7}
- Add the first and second elements: {2, 3}
- Add the first and third elements: {2, 5}
- Add the first and fourth elements: {2, 7}
- Add the second and third elements: {3, 5}
- Add the second and fourth elements: {3, 7}
- Add the third and fourth elements: {5, 7}
- Add the first, second, and third elements: {2, 3, 5}
- Add the first, second, and fourth elements: {2, 3, 7}
- Add the first, third, and fourth elements: {2, 5, 7}
- Add the second, third, and fourth elements: {3, 5, 7}
- Add all four elements: {2, 3, 5, 7}
Step 3: Combine all the subsets.
Combining all the individual subsets gives us the power set of the prime factors of 210:
{{}, {2}, {3}, {5}, {7}, {2, 3}, {2, 5}, {2, 7}, {3, 5}, {3, 7}, {5, 7}, {2, 3, 5}, {2, 3, 7}, {2, 5, 7}, {3, 5, 7}, {2, 3, 5, 7}}
Thus, the power set of the prime factors of 210 is {{}, {2}, {3}, {5}, {7}, {2, 3}, {2, 5}, {2, 7}, {3, 5}, {3, 7}, {5, 7}, {2, 3, 5}, {2, 3, 7}, {2, 5, 7}, {3, 5, 7}, {2, 3, 5, 7}}.