Exercise 277Logic, sets and proofs › Sets and mapsHigh schoolAdded 3 Nov 2026

Basic set operations

#sets#union#intersection#complement

Statement

Let $A=\{1,2,3,4\}$ , $B=\{3,4,5,6\}$ and the universe be $E=\{1,\ldots,8\}$ . Compute $A\cup B$ , $A\cap B$ , $A\setminus B$ , $A\triangle B$ , and $\overline{A}$ .

Hint

Union = all elements in at least one set; intersection = common elements; complement = elements of $E$ not in $A$ .

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Solution

Union. $A\cup B=\{1,2,3,4,5,6\}$ .

Intersection. $A\cap B=\{3,4\}$ .

Difference. $A\setminus B=\{1,2\}$ .

Symmetric difference. $A\triangle B=(A\setminus B)\cup(B\setminus A)=\{1,2,5,6\}$ .

Complement. $\overline{A}=E\setminus A=\{5,6,7,8\}$ .

Basic set operations

Statement

Solution

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