Question

Please help!! Will give brainiest!

Answer 1

1. B U C = {1, 2, 3, 4, 5, 6}

Why? Because all we're doing is combining the two sets B and C to form one bigger set. We toss out any duplicates. In this case, there aren't any duplicates to worry about. Set B contains {2,4,6} and set C has {1,3,5}, putting them together leads to {2,4,6,   1,3,5} which sorts to {1,2,3,4,5,6}. Sorting is optional but helpful. The "U" symbol represents "set union". The upside down version of this symbol means "set intersection".

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2. A intersect B = {2,4}

Note how the numbers 2 and 4 are in BOTH set A and set B at the same time. This is where the two sets overlap or intersect or what they have in common.

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3. A intersect C = {1,3,5}

Similar to problem 2 above. Set A and set C both have 1,3,5 in them and nothing else shared between the two sets.

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4. A intersect (B intersect C) = null or empty set

Start with comparing set B and set C. Note how they have nothing in common. We can replace "B intersect C" with "null set", as this is the empty set, ie there's nothing in here. We end up with "A intersect null set" which ultimately leads to the empty set as the final answer. The empty set is a subset of all sets. The null set can be written as $\varnothing$

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5. A U (B intersect C) = {1,2,3,4,5}

Back in problem 4 we saw that "B intersect C" reduced to the empty set. We can update problem 5 into "A U nullset" which simplifies to just set A. Unioning the empty set with any set leads to the original set. Its the same as saying "take a bucket of items and add nothing to that bucket, you will still have that original bucket of items".