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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.
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To help us find the value of 𝑥 in this problem, we’re given a subtraction.
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The first term in our subtraction is a set containing the elements nine and two.
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This is what it might look like as a diagram.
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Then, we’re told to subtract a set containing the elements 𝑥 and nine.
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But there’s something important to notice here.
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What we are left with, after we’ve subtracted 𝑥 and nine, is a null set.
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As what this symbol means, null sets are empty sets, and they don’t contain any elements at all.
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So, after we finish the subtraction, what we’re left with is no elements at all.
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This means that our subtraction can’t just include the number nine, but also has to include the number two.
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This then would leave us with our null set, our empty set.
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But we’re not told to subtract the elements nine and two.
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We’re told to subtract the elements 𝑥 and nine.
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Well, the two definitely goes because we’re left with nothing.
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So, we know that the letter 𝑥 must represent the number two.
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We started off with a set containing the elements nine and two.
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And we subtracted a set containing the elements 𝑥 and nine.
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Now, if 𝑥 is worth two, then we can subtract two, and also subtract nine.
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This leaves us with a set with nothing in it, an empty set, or a null set.
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And that’s how we know 𝑥 must equal two.