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Let A = {2, 3, 4, 5} and B = {0, 3, 6, 10, 12}

a) A U B. b) A n B. c) A - B. d) B - A.

User Hexalys
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Answers:

  • a) {0, 2, 3, 4, 5, 6, 10, 12}
  • b) { 3 }
  • c) { 2, 4, 5 }
  • d) { 0, 6, 10, 12}

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Step-by-step explanation:

The notation A U B means "set A union with set B". To union two sets, we combine them as one big set.

For example, {1,2,3} union with {a,b,c} becomes {1,2,3,a,b,c}

So {2,3,4,5} U {0,3,6,10,12} = {2,3,4,5,0,3,6,10,12} which sorts to {0,2,3,4,5,6,10,12}. Notice I tossed out that duplicate "3". We only list each unique value once

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A n B = intersection of A and B

We're looking for the numbers that are in both sets at the same time. In this case, only "3" is in both sets.

So A n B = { 3 }

Even though we have one value, we still use curly braces to denote we have a set.

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Now to compute A - B

Start with set A = {2, 3, 4, 5}

The erase any values that are found in set A n B. So we'll erase the "3"

Therefore, A-B = { 2, 4, 5}

This is basically another way of saying "start with set A, then kick out anything found in set B".

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Lastly, to compute B - A, we follow these steps

Start with B = {0, 3, 6, 10, 12}

Erase the items found in A n B = { 3 }

Therefore, B - A = { 0, 6, 10, 12 }

User Carnegie
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