2. A statement is a sentence which is either true or
false but not both.
Sentences which are questions, instructions and
exclamations are not statements.
eg : 8 + 2 = 10 (statement)
4 × 5 = 9 (statement)
2p = 4 (not a statement)
3. Write : i) a true statement and
ii) a false statement
involving the following numbers and
mathematical symbols.
eg : a) 1, 8 , 9, −, =
i) 9 − 8 = 1
ii) 1 − 9 = 8 or 8 − 9 = 1
or 1 − 8 = 9
4. ‘All’ includes every object that fulfils a specific
requirement.
‘Some’ includes a certain number of objects that
fulfils a specific requirement under
consideration.
eg : a) Fill in the correct quantifier :
i) All pentagons have five sides.
ii) Some prime numbers can be
divided by 2.
5. eg :
b) Determine the truth of the following
statements.
i) All triangles have one of its internal angles
equal to 900
. [True statement]
ii) Some numbers are negative.
[True statement]
iii) Some quadrilaterals have four sides.
[False statement]
6. Identifying two statements from compound
statement which contains the word ‘and’ or ‘or’
eg : a ) 2 and 7 are prime numbers.
Answer : 2 is prime number.
7 is prime number.
b) m + m + m = 3m or m × m = m
2
Answer : m + m + m = 3m
m × m = m
2
7. Determining the truth value of a compound
statement containing the word ‘and’ or ‘or’.
Truth table :
eg : a) 10 - 3 = 7 and 10
2
= 20
(T) (F) = F
b) 10 - 3 = 7 or 10
2
= 20
(T) (F) = T
Statement 1 Statement 2 and or
T T T T
T F F T
F T F T
F F F F
8. Constructing implications:
Eg: A polygon is a pentagon if and only if it has five sides.
Answer:
Implication 1: If a polygon has five sides, then it is a
pentagon.
Implication 2: If a polygon is a pentagon, then it has five
sides.
Antecedent and consequence.
Eg: If 2x = 4, then x = 2.
Antecedent consequence.
9. Three forms of arguments.
Form Argument Eg
1 Premise 1: All A are B.
Premise 2 : C is A.
Conclusion: C is B.
Premise 1: All isosceles triangles have two
equal sides.
Premise 2 : ABC is an isosceles triangle.
Conclusion: ABC has two equal sides.
2 Premise 1: If p, then q.
Premise 2: p is true.
Conclusion: q is true.
Premise 1: If m = 3, then m
3
= 27.
Premise 2 : m = 3.
Conclusion: m
3
= 27.
3 Premise 1: If p, then q.
Premise 2 : q is not true.
Conclusion: p is not true.
Premise 1: If m = 3, then m
3
= 27.
Premise 2 : m
3
≠ 27.
Conclusion: m ≠ 3.
10. Deduction is the process of making specific
conclusion based on a general statement.
Eg :
Given Tn = ar
n − 1
, given a = 3, r = 2 and n = 4.
Answer :
T4 = (3)(2)
4 − 1
= 24
11. Induction is the process of making a general
conclusion based on specific cases.
Eg : 2 = 4(1) − 2
6 = 4(2) − 2
10 = 4(3) − 2
…………..
Answer : 4n − 2, where n = 1, 2, 3, ………
