MediumMathematicsHigh School (11–12)Functions and Calculus › Sets and IntervalsNumerical

Let U = {1, 2, …, 12}, A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12}.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Let $U = \{1, 2, \ldots, 12\}$ , $A = \{2, 4, 6, 8, 10, 12\}$ and $B = \{3, 6, 9, 12\}$ . Find $(A \cup B)'$ and $A' \cap B'$ , and check that they are equal.

Need a reminder? The key ideaShow

$n(A \cup B) = n(A) + n(B) - n(A \cap B)$ . A set of $n$ elements has $2^n$ subsets. De Morgan: $(A \cup B)' = A' \cap B'$ and $(A \cap B)' = A' \cup B'$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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