4.1 Statements

(A) Determine Whether a Given Sentence is a Statement
1. A statement is a sentence which is either true or false but not both.

2. Sentences which are questions, instructions and exclamationsare not statements.

Example 1:
Determine whether the following sentences are statements or not. Give a reason for your answer.
(a) 3 + 3 = 8
(b) A pentagon has 5 sides.
(c) Is 40 divisible by 3?
(d) Find the perimeter of a square with each side of 4cm.
(e) Help!

Solution:
(a) Statement; it is a false statement.
(b) Statement; it is a true statement.
(c) Not a statement; it is a question.
(d) Not a statement; it is an instruction.
(e) Not a statement; it is an exclamation.



(B) Determine Whether a Statement is True or False.

Example 2:
Determine whether each of the following statements is true or false.
(a) 7 is a prime number
(b) -10 > -7
(c) 3 is a factor of 8.

Solution:
(a) True
(b) False
(c) False



(C) Constructing Statements Using Numbers and Symbols
 
1. True and false statements can be constructed with numbersand mathematical symbols.
 
Example 3:
Construct (i) a true statement, (ii) a false statement,
using the following numbers and mathematical symbols.
(a) 2, 4, 8, ×, =
(b) {a, b, c}, {d} , U =

Solution:
(a)(i) A true statement: 2 × 4 = 8
(a)(ii) A false statement: 2 × 8 = 4
(b)(i) A true statement: {d} U {a, b, c} = {a, b, c, d}
(b)(ii) A false statement: {d} U {a, b, c} = {d}



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