Complement and Difference

Let U = {$1$, $2$, $3$, $4$, $5$, $6$} and A = {$2$, $4$, $6$}. Find A′.

• 1List every element of U that is not in A.
• 2From U: $1$, $2$, $3$, $4$, $5$, $6$. Remove $2$, $4$, $6$.
• 3What remains: $1$, $3$, $5$

Answer: A′ = {$1$, $3$, $5$}

Let A = {$1$, $2$, $3$, $4$} and B = {$3$, $4$, $5$}. Find A − B.

• 1Start with every element of A: $1$, $2$, $3$, $4$.
• 2Remove anything that is also in B: remove $3$ and $4$.
• 3What remains: $1$, $2$

Answer: A − B = {$1$, $2$}

Using the same A and B, find B − A.

• 1Start with every element of B: $3$, $4$, $5$.
• 2Remove anything that is also in A: remove $3$ and $4$.
• 3What remains: $5$

Answer: B − A = {$5$} (note this is different from A − B)