Union and Intersection

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

• 1List every element that appears in A, in B, or in both.
• 2From A: $1$, $2$, $3$. From B: $3$, $4$, $5$.
• 3Combine, writing each element only once: $1$, $2$, $3$, $4$, $5$

Answer: A ∪ B = {$1$, $2$, $3$, $4$, $5$}

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

• 1Look for elements that appear in both sets.
• 2Compare: only $3$ appears in both A and B.

Answer: A ∩ B = {$3$}

Let C = {$1$, $2$} and D = {$5$, $6$}. Find C ∩ D.

• 1Compare every element: none of $1$ or $2$ appear in D.
• 2There is nothing shared.

Answer: C ∩ D = ∅ (C and D are called disjoint sets)