**High School Number Sense Lesson 107: Sets--Union and Intersection Combined**

This concept combines our understanding of

**SetsUnion**and

**SetsIntersect**. It appeared

**3 times**on this year’s test, with a median placement at

**question # 27**.

**Like our Facebook Page (**

**https://www.facebook.com/numberdojo/**

**) if you want to see new number sense posts on your wall. I will reward you with a free concept index or flashcard file of your choice. Thank you!**

**Number Dojo Level: TBD**

Instead of identifying the elements in the

**union**and also identifying the elements in the

**intersection**of two sets, sometimes we can use this quick fact:

**n(A) + n(B) = n(A**

**U B) + n(A**

**∩**

**B)**

**A plus**the number of elements in set

**B**is

**equal to**the number of elements in their

**union plus**the number of elements in their

**intersection**.

Let’s try it out…say set A = {1,2,3,4,5} and set B = {2,3,5,7,11}.

- n(A) = 5
- n(B) = 5
- n(A U B) = n(1,2,3,4,5,7,11) = 7
- n(A
**∩**B) = n(2,3,5) = 3 - 5 + 5 = 7 + 3 CORRECT

**Example 1: If set A = {p,a,r,k,s} and set B = {h,a,w,k,s}, then n(A**

**U B) + n(A**

**∩**

**B) = ___**

- Just count the number of elements in sets A and B, and add them.
- 5 + 5 =
**10**

**Example 2: If there are 8 elements in set A, 6 in set B, and 12 in A**

**U B, then A**

**∩**

**B has ___ elements**

- 8 + 6 = 12 + ___
- The answer is
**2**

**Example 3: Set A has 6 elements and set B has 8 elements. If A**

**∩**

**B has 4 elements, then A**

**U B has ___ elements**

- 6 + 8 = 4 + ___
- The answer is
**10**

**Example 4: ({p,l,u,s}**

**U {m,i,n,u,s})**

**∩**

**{t,i,m,e,s} has ___ distinct elements**

- Take note of the () around the first two sets; start here.
- {p,l,u,s} U {m,i,n,u,s} has
**7**elements: {p,l,u,s,m,i,n} - {p,l,u,s,m,i,n}
**∩**{t,i,m,e,s} = {s,m,i}—so**3**elements

**Example 5: Let U = {u,n,o}, D = {d,o,s}, T = {t,r,e,s} and C = {c,u,a,t,r,o}. The number of distinct elements of (U**

**U T)**

**∩**

**(D**

**È C) is ___**

- Be careful with the order!
- {u,n,o} U {t,r,e,s} = {u,n,o,t,r,e,s}
- {d,o,s} U {c,u,a,t,r,o} = {d,o,s,c,u,a,t,r}
- {u,n,o,t,r,e,s}
**∩**{d,o,s,c,u,a,t,r} = {u,o,t,r,s}—so**5**elements

**Up Next for High School: Base2toBase8**