3-5 Working With Sets

3-5 Working With Sets

Page 194

10/20/20

Open Ended

What is a word that you could be trying to spell?

Roster form lists the elements of a set within braces, { }.

The set of 1 and 2 {1,2)

The set of multiples of 2 {2, 4, 6, 8, . . .}

Set-builder notation describes the properties an element must have to be included in a set.

{x | x is a multiple of 2} is read as "the set of all real numbers x, such that x is a multiple of 2."

Multiple Choice

The solutions of the inequality in set-builder notation.

2y + 5 < 21

• {y l y < 8}

• {y l y < 16}

• {y l y < 23}

• {y l y < -8}

 $A\subseteq B$  means A is a subset of B
All of the elements in A are also in B

The empty set, or null set, is the set that contains no elements.

The empty set is a subset of every set.

To represent the empty set use

 $\phi$  or $\left\{\right\}$  

Multiple Choice

What are the numbers in a set called?

• options

• elements

• parts

Multiple Choice

True or False? {A,B} is subset from {A,B,C,D}

• True

• False

Multiple Select

Every set has _____ as one of its subsets (select all that apply.)

• ∅

• 0

• itself

• the real numbers

Multiple Choice

How many subsets does set A = { red, blue} has?

• 1

• 2

• 3

• 4

Multiple Choice

If P = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of P.

• A = {2, 4}

• B = {13, 7, 9, 11, 5, 3, 1}

• C = {2, 3, 4, 5}

• D = {0}

The universal set or universe is the largest set you are working with.

The complement of a set is the set of all elements in the universe that are not in the set. The complement of A is A'

The universe is all possible numbers that you can roll on a die.

Open Ended

Multiple Choice

• whole numbers
• natural numbers
• integers
• rational numbers

Multiple Choice

The Universal Set = { -4, 3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.
What is the complement of A?

• {-4, -3, -2, -1, 0, 1, 2, 3}
• {-3, -2, -1, 1, 2, 3}
• {-4, -3, -2, -1, 1, 2, 3, 4}
• {-4, -3, -2, -1, 1, 2, 3}

Multiple Choice

If

U (the universal set) = {1, 3, 5, 7, 9, 11, 13, 15, 17} and W = {5, 7, 9, 11}, then W' = . . ..

• {1, 3, 13, 15, 17}

• {1, 3}

• {2, 4, 6, 8, 10, 12, 14, 16}

• {1, 3, 5, 7, 9, 11, 13, 15, 17}

Multiple Choice

Write each set in roster form and in set-builder notation.

• {0,1,2,3} ; {n | n is an integer, -1 < n < 4}
  

• {1,2,3,4,6,12} ; {n | n is a real number that is a factor of 12}

• {1,2,3,4,5,6,7,8,9,10} ; {n | n is a natural number, n < 11}

• $\varnothing$ ; {n | n is an even natural number, n < 2}
  

Multiple Choice

A={x : x is a prime number less than 20}

• {2,3,5,7,11,13,17,19}

• {1,2,3,5,7,11,13,17,19}

• {2,3,5,7,9,11,13,17,19}

• {2,3,5,7,11,13,15,17,19}

3-6 Compound Inequalities

page 200

10/21/20

A compound inequality consists of two distinct inequalities joined by the word and or the word or.

You can write a compound inequality involving and as a single inequality.

x > 4 and x < 9 can be written as 4 < x < 9.

Multiple Choice

What inequality is graphed? 

• x > 2 and x ≤ -3
• x > 2 and x < -3
• x > 2 or x ≤ -3
• x > 2 or x < -3

Multiple Choice

What inequality is graphed?

• x > 2 and x < 4
• x ≥ 2 and x ≤ 4
• x > 2 or x < 4
• x ≥ 2 or x ≤ 4

Multiple Choice

x+2<-4 or -5x<-15

• -6<x<3
• x<-3 and x>6
• x<-6 or x>3
• No Solution

Multiple Choice

Write an inequality for Graph 3.

• x ≤ -2 AND x > 5
• x ≤ -2 OR x > 5
• x ≥ -2 OR x < 5
• -2 ≤ x < 5