Q:

What is the solution set for the open sentence with the given replacement set? 2t-t=0,{1,2,3,4}A. Null setB. 2C. 3D. 4

Accepted Solution

A:
Answer is choice A, the null set

This is another way of saying "the empty set" which is the set of nothing inside it. It's a fancy mathematical way of saying "no solutions" in terms of the given restrictions placed upon us.

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Let's check every value in the replacement set. All we do is go through each number one at a time

Checking t = 1
2t - t = 0
2*1 - 1 = 0 ... replace every t with 1
2 - 1 = 0
1 = 0
The last equation is false so we can cross t=1 off the list
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Checking t = 2
2t - t = 0
2*2 - 2 = 0 ... replace every t with 2
4 - 2 = 0
2 = 0
The last equation is false so we can cross t=2 off the list
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Checking t = 3
2t - t = 0
2*3 - 3 = 0 ... replace every t with 3
6 - 3 = 0
3 = 0
The last equation is false so we can cross t=3 off the list
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Checking t = 4
2t - t = 0
2*4 - 4 = 0 ... replace every t with 4
8 - 4 = 0
4 = 0
The last equation is false so we can cross t=4 off the list
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We've crossed everything off the list. So there are no solutions indicating the solution set is the null set or empty set.

Side Note: if t = 0 were in the replacement set, then we'd have a solution. However that isn't the case here.