Find the power sets of the following.
i) A=∅
b) B = {1,2)
ii) C = {p, q. r}
Answers
Answer:
The Power Set can be useful in unexpected areas.
I wanted to find all factors (not just the prime factors, but all factors) of a number.
I could test all possible numbers: I could check 2, 3, 4, 5, 6, 7, etc...
That took a long time for large numbers.
But could I try to combine the prime factors?
Let me see, the prime factors of 510 are 2×3×5×17 (using prime factor tool).
So, all the factors of 510 are:
2, 3, 5 and 17,
2×3, 2×5 and 2×17 as well, and
2×3×5 and 2×3×17 and ...
.. aha! Just like ice cream I needed a Power Set!
And this is what I got:
2,3,5,17 Subset Factors of 510
0 0000 { } 1
1 0001 {17} 17
2 0010 {5} 5
3 0011 {5,17} 5 × 17 = 85
4 0100 {3} 3
5 0101 {3,17} 3 × 17 = 51
... etc ... ... etc ... ... etc ...
15 1111 {2,3,5,17} 2 × 3 × 5 × 17 = 510
And the result? The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255 and 510 (and −1, −2, −3, etc as well). See the All Factors Tool.
Step-by-step explanation:
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Answer:
1) { }
2) {1},{2},{ }
3) {p},{q},{r},{p,r},{p,q},{q,r},{ }
I hope it is helpful.
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