Form 4 Mathematics Bab 3: Logical Reasoning
Instructions
Answer all questions clearly. Write down precise premises, implications, or conclusions as required.
10 questions · 22 marks total
1. Observe the numerical pattern below:
1 = 2(1) - 1
3 = 2(2) - 1
5 = 2(3) - 1
7 = 2(4) - 1
(a) Make a general conclusion by induction for the sequence of odd numbers.
(b) Use your conclusion from (a) to calculate the 50th term of this sequence.
2. True or False: Inductive reasoning guarantees that its conclusion is 100% true in all cases.
True / False · 1m3. For the implication 'If x = 4, then 3x + 2 = 14', construct:
(a) the Converse,
(b) the Inverse,
(c) the Contrapositive.
4. Which of the following represents the inverse of 'If p, then q'?
Multiple Choice · 1m5. Fill in the blank: An implication 'If p, then q' and its ________ always have the same truth value.
Fill in the Blank · 1m6. Complete the following deductive arguments:
(a) Premise 1: All prime numbers greater than 2 are odd numbers.
Premise 2: 13 is a prime number greater than 2.
Conclusion: ________
(b) Premise 1: If a quadrilateral is a square, then it has 4 equal sides.
Premise 2: ________
Conclusion: Quadrilateral ABCD does not have 4 equal sides.
7. Determine whether the following compound statement is True or False:
'8 is an even number AND 8 is a prime number.'
8. True or False: The sentence 'x² - 4 = 0' is a statement.
True / False · 1m9. Write the negation of the statement '25 is a perfect square' and state its truth value.
Short Answer · 2m10. Form two implications from the biconditional statement:
'A polygon is a regular polygon if and only if all its sides and angles are equal.'