n is an even number

• closed sentence
• open sentence

A sentence is _____ when it is not known if it is true or false.

• open

8 is an even number

• closed sentence
• open sentence

9 is an even number

• closed sentence
• open sentence

An expression does state a complete thought;

*All UP students are intelligent. • Juan is a PUP student. • Therefore, Juan is intelligent.

• deductive

from specific to general reasoning

• inductive

A mathematical ________ is the analogue of an English sentence; it is a correct arrangement of mathematical symbols that states a complete thought.

• sentence

‘x=2’ is sometimes true/sometimes false: it is ____when xx is 2, and _____ otherwise.

• true then false
• false then true

The most common expression types are what?

• numbers, sets, and functions

is the sentence true or false 25+60=85

• true
• false

2 types of reasoning

• deductive, inductive

• inductive, deductive

Characteristics of Modern Mathematics

• Applicability and Effectiveness, Abstraction and Generality, Simplicity, Logical Derivation, Axiomatic Arrangement, Precision, Correctness, Evolution through Dialect

*True or False Test is not difficult. • Multiple Choice Test is not difficult. • Therefore, all tests are not difficult.

• inductive

what type of reasoning is this. 2 is an even number • 12 is an even number. • 22 is an even number. • Therefore, all numbers ending with 2 are even numbers.

• inductive

An ________ is the mathematical analogue of an English noun; it is a correct arrangement of mathematical symbols used to represent a mathematical object of interest.

• expression

‘x+3=3+x’ is (always) true or false?

• true

A _______ sentence is always true (or always false).

• closed

• closed sentence

is the sentence true or false. 12+34=45

• true
• false

from general to specific reasoning

• deductive