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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?

 Nov 20, 2019
 #1
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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 -1both create negative values.

 

Since there are negative values.

 

15 - 2 = THE ANSWER?

 

 

 

 

We check with a table

x valuesy valuesxy
-1-21
1-11
201
-11-1
121
2-21/4
-1-1-1
101
212
-121
1-21
2-11/2
-101
111
224

 

BUT WAIT! They said distinct.

 

So count the distinct values in the table, and you should get the answer.

 Nov 20, 2019
edited by CalculatorUser  Nov 20, 2019

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