If $U = \{1, 2, 3, 4, 5, 6\}$, $A = \{2, 3\}$ and $B = \{3, 4, 5\}$, then find $A'$ and $B'$.

**OR**

If $A = \{1, 2, 3, 4, 5, 6\}$, $B = \{2, 4, 6, 8\}$, then find $A - B$ and $B - A$.

Question

If $U = \{1, 2, 3, 4, 5, 6\}$, $A = \{2, 3\}$ and $B = \{3, 4, 5\}$, then find $A'$ and $B'$.

**OR**

If $A = \{1, 2, 3, 4, 5, 6\}$, $B = \{2, 4, 6, 8\}$, then find $A - B$ and $B - A$.

Accepted Answer

>

> [!TLDR]
> $A' = U - A$ and $B' = U - B$; listing the elements of U not present in each set gives the complements.
>
> Given $U=\{1,2,3,4,5,6\}$, $A=\{2,3\}$, $B=\{3,4,5\}$.
>
> $A' = U - A$: remove 2 and 3 from U, leaving $A' = \{1,4,5,6\}$.
> …

Operation	What it asks	Bucket contains
Union ( $A \cup B$ )	In either?	Everything from $A$ or $B$ (or both)
Intersection ( $A \cap B$ )	In both?	Only the overlap
Difference ( $A \setminus B$ )	In $A$ but not $B$ ?	Just the part of $A$ that doesn't touch $B$
Complement ( $A^c$ )	Not in $A$ ?	Everything outside $A$ (inside $U$ )
Symmetric Difference ( $A \triangle B$ )	In exactly one?	The two crescent-shaped parts, excluding the overlap

Q.If $U = \{1, 2, 3, 4, 5, 6\}$ , $A = \{2, 3\}$ and $B = \{3, 4, 5\}$ , then find $A'$ and $B'$ . OR If $A = \{1, 2, 3, 4, 5, 6\}$ , $B = \{2, 4, 6, 8\}$ , then find $A - B$ and $B - A$ .

Concept understanding — Set Operations

The idea in plain words

Why this works

Step by step

A common slip …

🎓Unlock everything free for 14 days

Unlock everything free for 14 days