conjunctions - whiteplainspublicschools.org€¦  · web viewa compound sentence is a sentence...

Day 4: Solving Compound InequalitiesWarm Up

0

Vocabulary

compound inequality

conjunction

disjunction

A compound sentence is a sentence that combines two simple sentences using the word AND or the word OR. These sentences can be true or false depending on the sentences themselves and which word joins the sentences together.

Exercise

Consider the following compound sentences. Tell whether they are true or false.

19

Think and Write

When is a sentence containing the word AND true? _______________________

________________________________________________________________

When is a sentence containing the word OR true? ________________________

________________________________________________________________

Conjunctions

A statement that combines two inequalities using AND is called a conjunction.

The graph of a conjunction is the overlapping region, or intersection, between the two individual inequalities.

Example

Two ways to write this conjunction are:

20

Exercise A

x<5

x>2

x<5∧x>2

This conjunction is equivalent to: ____________________________________

x≥−4

x≤−1

x≥−4∧x ≤−1

This conjunction is equivalent to: ____________________________________

x<3

x≥−1

x<3∧x ≥−1

This conjunction is equivalent to: _____________________________________

Note: The symbol for the word “and” is ∧.

21

Exercise B

f. Write a conjunction that is illustrated by the graph below in two ways:

_________________________________ ________________________________

22

____________ and ____________

Compound sentence: ____________ and ____________

Disjunctions

A statement that combines two inequalities using OR is called a disjunction.

The graph of a disjunction is the region formed when the graphs of the two individual inequalities are combined. We shade the regions that are shaded at least once. This combined region is called the union of the sets.

Example

Note: The symbol for the word “or” is ∨ .

23

Exercise A

x>1

x<−3

x>1∨x<−3

This disjunction is equivalent to: __________________________________________

x>0

x≤−2

x>0∨x ≤−2

This disjunction is equivalent to: _________________________________________

x≤−2

x≥3

x≤−2∨x ≥3

This disjunction is equivalent to: _________________________________________

24

Exercise B

1) Graph the following compound sentence on the number line below.

2) Is the following sentence true or false? Explain your reasoning.

3) . Write a compound inequality for the graph shown below.

_____________________________

4)

Name another inequality that is equivalent to the compound inequality you just graphed.

25

Summary

Conjunctions

A conjunction is a compound sentence joined by AND. The solution set of a conjunction is the set of values that make both inequalities true. This set is also called the intersection of the two solution sets. On a graph, it is the area where the two individual graphs overlap.

Disjunctions

A disjunction is a compound sentence joined by OR. The solution set of a disjunction is the set of values that make either inequality true (or both). This set is also called the union of the two solution sets. On a graph, it is the total area shaded by the two individual graphs.

26

Homework

27