Video: Using the Understanding of Operations on Sets to Find Unknowns

Given {9, 2} − {𝑥, 9} = ∅, find the value of 𝑥.

01:50

Video Transcript

Given a set containing the elements nine and two take away a set containing the elements 𝑥 and nine equals a null set, find the value of 𝑥.

To help us find the value of 𝑥 in this problem, we’re given a subtraction. The first term in our subtraction is a set containing the elements nine and two. This is what it might look like as a diagram. Then, we’re told to subtract a set containing the elements 𝑥 and nine. But there’s something important to notice here. What we are left with, after we’ve subtracted 𝑥 and nine, is a null set. As what this symbol means, null sets are empty sets, and they don’t contain any elements at all.

So, after we finish the subtraction, what we’re left with is no elements at all. This means that our subtraction can’t just include the number nine, but also has to include the number two. This then would leave us with our null set, our empty set. But we’re not told to subtract the elements nine and two. We’re told to subtract the elements 𝑥 and nine. Well, the two definitely goes because we’re left with nothing. So, we know that the letter 𝑥 must represent the number two.

We started off with a set containing the elements nine and two. And we subtracted a set containing the elements 𝑥 and nine. Now, if 𝑥 is worth two, then we can subtract two, and also subtract nine. This leaves us with a set with nothing in it, an empty set, or a null set. And that’s how we know 𝑥 must equal two.

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