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

Let A = {a, b, {c, d}}. Say which of these are true.

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

Let $A = \{a, b, \{c, d\}\}$ . Say which of these are true.

$\{c, d\} \in A$

$\{c, d\} \subseteq A$

$\{a, b\} \subseteq A$

$c \in A$

$\varnothing \subseteq A$

How many elements does $A$ have?

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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