Worksheet Chapter 3: Logical Reasoning

1. Which of the following represents the inverse of 'If p, then q'?

2. Write the negation of the statement '25 is a perfect square' and state its truth value.

3. True or False: The sentence 'x² - 4 = 0' is a statement.

4. Fill in the blank: An implication 'If p, then q' and its ________ always have the same truth value.

5. 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.

6. Determine whether the following compound statement is True or False: '8 is an even number AND 8 is a prime number.'

7. Form two implications from the biconditional statement: 'A polygon is a regular polygon if and only if all its sides and angles are equal.'

8. For the implication 'If x = 4, then 3x + 2 = 14', construct: (a) the Converse, (b) the Inverse, (c) the Contrapositive.

9. True or False: Inductive reasoning guarantees that its conclusion is 100% true in all cases.

10. 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.