LOGICAL REASONING

Mathematical Reasoning

LOGICAL
REASONING

Mathematical Reasoning

1. Are the sentences below a statement or non- 2. State whether the following statements are true or 3. Complete the following statement using the
false. quantifier “all” or “some” to make it a true
statement? i. All multiples of 6 are multiples of 12.
ii. 9 is a prime number and 7 is a perfect square. statement.
i. 57 is a perfect square iii. 57 is an odd number …………. pyramids have a rectangular base.
ii. > 0 iv. 119 is a prime number …………. multiples of 3 are multiples of 8.
iii. −5 < −7 v. + 3 = 10
iv. 4 − 8 + 7 4. State the converse of the following statement and
v. 2 − 3 = 2
vi. 6 > 3√125 hence determine whether its converse is true of

false.

> , >

5. Complete the premise in the following statement. 6. Complete the premise in the following argument. 7. Complete the premise in the following argument.
Premise 1: ………………………………………. Premise 1: ……………………………………. Premise 1: if x is an even number, then x + 1 is an
…………………………………………. …………………………………….
odd number
Premise 2: Solid X is a prism. Premise 2: ≠ 3 Premise 2: ……………………………………….
Conclusion: 3 ≠ 27
Conclusion: Solid X has a uniform cross-section. Conclusion: 7 is an odd number.

8. Write down Premise 2 to complete the argument. 9. Write down Premise 1 to complete the argument. 10. Write down Premise 2 to complete the argument.
Premise 1: < 0, ℎ − 4 > 0. Premise 1: ………………………………………. Premise 1: = 7, ℎ 3 − 5 = 16
Premise 2: ………………………………………. ……………………………………… Premise 2: ……………………………………….
Conclusion: 3 > 0 Conclusion: 3 − 5 = 16
Premise 2: 3 is not an even number.
11. Form a general conclusion by induction for the 13. Form a general conclusion by induction for the
following number sequence -1, 5, 15, 29, … which Conclusion: 3 cannot be divisible by 2 following number sequence 5, 17, 45, 113, …
follows the pattern: which follows the pattern:
−1 = 2(1) − 3 12. Form a general conclusion by induction for the 5 = 2(1) + 3
5 = 2(4) − 3 following number sequence 1, 22, 79, 190, … 17 = 2(4) + 9
15 = 2(9) − 3 which follows the pattern: 45 = 2(9) + 27
29 = 2(16) − 3 1 = 3(1) − 2 113 = 2(16) + 81
22 = 3(8) − 2
79 = 3(27) − 2
190 = 3(64) − 2

………………… ………………… …………………

14. Form a general conclusion by induction for the 15. Combine the following pair of statements to form a 16. Combine the following pair of statements to form a
following number sequence 7, 44, 143, 336, … true statement. false statement.
which follows the pattern: Statement 1: 42 = 8 Statement 1: sin 30° = 1
7 = 5(1) + 2 Statement 2: (52)3 = 56
44 = 5(8) + 4 Statement 2: 4 × 5 = 20 …………………………………………………….
143 = 5(27) + 8 ……………………………………………………..
336 = 5(64) + 16

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Mathematical Reasoning

Mathematical Reasoning

Mathematical Reasoning