Video: Finding an Unknown Element Using the Union of Sets

Given that {6, 7} ∪ {1, 8} = {7, 8, 𝑥, 6}, what is the value of 𝑥?

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Video Transcript

Given that the union of six and seven and one and eight is equal to the set seven, eight, 𝑥, six, what is the value of 𝑥?

First, let’s begin by understanding what this union symbol means. The union of two sets is the elements that belong to both sets or either set. So what elements are in both sets? Well, there’s six and seven in one set and one and eight in another set. So they don’t have any that are in both of them. But we also have to list the elements that are in either set.

So six and seven are in one set. And one and eight are- are in another set. But we also know that we need to set this equal to the set seven, eight, 𝑥, and six. And we can solve for 𝑥. So they both list element six. They both list element seven. And they both list element eight. So the only thing that’s left would be one and 𝑥. Therefore, 𝑥 must be equal to one.

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