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MATHEMATICAL REASONING

CHAPTER

4

MATHEMATICS FORM 4

STATEMENT AND QUANTIFIERS

LEARNING OUTCOMES

By the end of the lesson, student should be able to:

(a)Determine whether a given sentence is statement and that statement is true or false.

(c) Construct true or false statements using given numbers and mathematical symbol.

(d) Construct statement using quantifier all and some.

(e) Determine whether a statement that contains the quantifier “all” is true or false.

(f) Construct a true statement using the quantifier “all” or “some” given an object and a property.

A statement is a sentence that is either TRUE or FALSE but not both.

Look at these Lemang! They are baked in bamboo. Lemang is made up of rice and water. Am I right, uncle?

No, it is made up of glutinous rice and coconut milk. Is it your favourite dish on Hari Raya?

Yes, I love to eat Lemang very much.

STATEMENT NOT STATEMENTThey are baked in bamboo.

Look at these Lemang!

Lemang is made up of rice and water.

Is it your favourite dish on Hari Raya?

No, it is made up of glutinous rice and coconut milk.

-

Yes, I love to eat Lemang very much.

-

STATEMENTSTATEMENT

TRUETRUE FALSEFALSE

WORDS

WORDS + NUMBERS

NUMBERS + MATH SYMBOL

Five is greater than three

5 is greater than 3

5 > 3

Statement can be written in 3 ways

Words

Numbers Words Numbers

Numbers Mathematical symbol Numbers

Singapore is an island

6 is greater than 7

23 = 32

Malaysia is an island

The third significant figure of 1.079 is 7

15 > -15

True statement

True statement

True statement

False

statement

False statement

False statement

WordsNumbers & Words

Numbers & Symbols

x + 3 = 5

x2 – y2 = 3BOTH ARE NOT STATEMENT!

Because it can either be true of false depending on the value of x

and y

•Come here!

•How old are you?

•X + 2 = 5• y + 3x

COMMAND

QUESTION

EQUATIONS

NOT STATEMENT

Construct statement using numbers and mathematical symbol

4 , 7, >True

7 > 4

15 ÷ 5 = 3

-5 x 2 < 1 x 8

True

True

False

False

False

4 > 7

15, 5, 3, ÷, = 5 ÷ 15 =

3

1, 8, -5, 2, x, <

1 x 8 < -5 x 2

All animals have legs

All birds can fly

Quantifiers ‘ALL’ and ‘SOME’Specify quantity or number of objects

FALSE

TRUE

FALSE

All positive numbers are

greater than 0Some of us have been selected to join PLKN

TRUE

Some empty sets have elementsFALSE

MORE QUANTIFIERSEach

ALL

Most

Many Every

None

A lot of

A few

Several

Any

Part of

SOME

Any positive numbers are greater than 0

Any positive numbers are greater than 0

All positive numbers are

greater than 0

Some of us have been selected to join PLKN

USING MORE QUANTIFIERS

Only a few or several has been selected to join PLKN

Only a few or several has been selected to join PLKN

OBJECT PROPERTY TRUE STATEMENT

Construct a true statement using the quantifier “all” or “some” given an object and a property

Trapezium

Diagonals of squares

Months

A pair of parallel sides

Bisect each other at 90o

Have 30 days

All trapeziums have a pair

of parallel sidesAll diagonals of Squares bisect each other at 90o

Some monthshave 30 days

A statement is a sentence that is either true or false but not both simultaneously.

Example:

8 x 2 = 16

4 – 2 = 3

4x + 5

Statement is true

Statement is false

Not a statement

STATEMENT

Quantifiers are used to indicate the number of cases there are in a statement.

• “ALL” indicates each and every one

• “SOME” indicates at least one or several.

Example:

1) All octagons have 8 sides.

2) Some triangles have equal sides.

QUANTIFIERS [“ALL” or “some”]