If x is an element of the set {-1, 1, 2} and y is an element of the set {-2, -1, 0, 1, 2}, how many distinct values of x^y are positive?
+2863 The only way to get the answer is to read the explanation ENTIRELY
List this out, trust me, it won't take long.
We see that there are 3 * 5 = 15 total possible values of x^y.
We find all the number of values that are NEGATIVE, then subtract that number from 15.
Looking at the y sets, we see that anything value of y that is -2, 0, 2, will create positive values no matter what.
So the y values can be -1 or 1.
There is only one x-value that has potential to be negative, and that is -1.
We see that -1-1 and -11 both create negative values.
Since there are 2 negative values.
15 - 2 = THE ANSWER?
We check with a table
| x values | y values | xy |
| -1 | -2 | 1 |
| 1 | -1 | 1 |
| 2 | 0 | 1 |
| -1 | 1 | -1 |
| 1 | 2 | 1 |
| 2 | -2 | 1/4 |
| -1 | -1 | -1 |
| 1 | 0 | 1 |
| 2 | 1 | 2 |
| -1 | 2 | 1 |
| 1 | -2 | 1 |
| 2 | -1 | 1/2 |
| -1 | 0 | 1 |
| 1 | 1 | 1 |
| 2 | 2 | 4 |
BUT WAIT! They said distinct.
So count the distinct values in the table, and you should get the answer.
