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?

Guest Nov 20, 2019

#1**+3 **

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 -1^{1 }both create negative values.

Since there are **2 **negative values.

15 - 2 = THE ANSWER?

We check with a table

x values | y values | x^{y} |

-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.

CalculatorUser Nov 20, 2019