Consider the universe $U=\{x | x \in \mathbb{Z}, 1 \le x \le 10\}$ and the following subsets of $U$ $A = \{ 2,5,9 \}$
$B = \{ 1,4,7,8,10 \}$
$C = \{ 1,2 \}$
In the following questions we denote $A′$ the complement of $A$. i.e. $A' = U - A$


*

*$A′$

*$A \cup B \cup C$

*$B′  −  A$

*$A  \bigtriangleup  B$
I can't access my notes and finding this hard to work out. Thanks.

*

*$A' = U - A.$

*$A \cup B \cup C = \{x\lvert\, x\in A \lor x\in B \lor x\in C\}.$

*$B' - A = (U-B)-A.$ 

*$A\Delta B = \{x\lvert\,(x\in A \lor x\in B)\land x\notin (A \cap B)\}=\{x\lvert\, x\in (A\cup B) \land x \notin (A\cap B)\}.$


I will do 1, you can probably do the rest from here.
$U=\{1,2,3,4,5,6,7,8,9,10\}$. So $A'=U-A=U -\{2,5,9\}=\{1,3,4,6,7,8,10\}.$
Here are the Venn diagrams of the sets:
(1) is not A, (2) is A or B or C, (3) is not B minus A, (4) is A iff not B.

