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If π is the set of elements eight, six, and two and π is the set of elements seven, three, and nine, which Venn diagram represents the two sets?
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Letβs begin by going through each option and seeing what they entail.
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For option a, we have the π elements, the π elements, and this portion is the π and π elements, so the elements that are in both.
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Itβs called the intersection of the sets.
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For option b, π is the entire box.
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So any number that is in this box is in the set.
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And then π are all of the elements inside of the circle.
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But notice the circle is inside of the box.
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Which means all of the elements of π must be in π.
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So π would be a subset of π.
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For option c, π and π are represented by the entire circle.
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Which means they share all of the exact same elements.
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And then for option d, set π and set π are totally separate and they donβt overlap.
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Meaning, they donβt have any elements in common.
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So letβs begin by looking at set π and π and determine which one a, b, c, or d would be the best Venn diagram to represent the two sets.
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So π holds the elements eight, six, and two.
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π holds the elements of seven, three, and nine.
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So right away, what is their intersection?
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What do they have in common?
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Do they have any elements in common?
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They donβt.
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So their intersection would be the empty set.
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So that means we can eliminate option a because it says that they share elements two and seven.
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And they donβt.
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Two is in the set π and seven is in the set π.
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But itβs not in both.
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So if we know that they donβt have any elements in common, this can actually go pretty quickly.
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Because option b is saying that all of the elements in π are actually also in π.
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And thatβs not the case.
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None of πβs elements are actually in π.
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And then for option c, it says that they have the exact same elements, that they all have elements eight, two, seven, three, six, and nine.
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And actually, π and π each only have three elements.
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So this leaves us with option d.
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It says that set π should have elements two, which it does, six, and eight.
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And thatβs great for π.
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And then π should have nine, seven, and three.
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And none of these are the same.
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So they shouldnβt overlap.
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So this means the best Venn diagram to represent the two sets would be option d.