Logical Reasoning

Question 10:(a)(i) State whether the following compound statement is true or false.   All straight lines have positive gradients.(ii) Write down the converse of the following implication.If x = 5, then x2 = 25.(b) Write down Premise 2 to complete the following argument:Premise 1: If Q is an odd number, then 2 × Q is an … Read more

Question 8:(a) State whether the following sentence is a statement or not a statement. x + 7 = 9(b) Complete the following compound statement by writing the word ‘or’ or ‘and’ to form a true statement.23 = 6 …… 5 × 0 = 0(c) Write down Premise 2 to complete the following argument:Premise 1: All … Read more

Question 6: (a) Complete the following mathematical sentence by writing the symbol > or <.   (i) 53____ 20 is a false statement.   (ii) – 3 ____ – 10 is a true statement. (b) Complete the conclusion in the following argument:  Premise 1 : If  n 1 2 = n , then  4 1 2 = 4 =2.   Premise 2 :  … Read more

Question 4: (a) Combine the following two statements to form one true statement.   Statement 1: (– 3)² = 9   Statement 2: –3 (3) = 19 (b) Complete the premise in the following argument: Premise 1: _____________________ Premise 2: x is a multiple of 25. Conclusion: x is a divisible of 5. (c) Make a … Read more

Question 1: (a) State if each of the following statements is true or false.  (i) (i)  2 4 =16  and  12÷ 27 3 =3.  (ii) 17 is a prime number or an even number. (b) Complete the statement, in the answer space, to form a true statement by using the quantifier ‘all’ or ‘some’. (c) Write down two … Read more

3.6 Deduction and Induction (A) Reasoning by Deduction and Induction 1. Reasoning by deduction is a process of making a conclusion for a specific case based on a given general statement. 2. Reasoning by induction is a process of making a generalization based on specific cases. Maths Tip 1. General statement  →  Special conclusion  → Deduction 2. … Read more

Example 1: Complete the conclusion in the following argument: Premise 1: All regular polygons have equal sides. Premise 2: ABCD is a regular polygon. Conclusion: Solution: Conclusion: ABCD has equal sides. Example 2: Complete the conclusion in the following argument: Premise 1: If m > 4, then 2m > 8. Premise 2: 2m < 8 … Read more

3.5 Arguments (A) Premises and Conclusions 1. An argument is a process of making conclusion based on several given statements. 2. The statements given are known as premises. 3. An argument consists of premises and a conclusion. Example 1: Identify the premises and conclusion of the following argument. (a) A pentagon has 5 sides. ABCDE … Read more

Example 1: Write down two implications based on the following statement. y3 = -125 if and only if y = -5. Solution: Implication 1: If y3 = -125, then y = -5. Implication 2: If y = -5, then y3 = -125.  Example 2: Write down two implications based on the following statement. 8 is … Read more

3.4 Implications (A) Antecedent and Consequent of an Implication 1. For two statements p and q, the sentence ‘if p, then q’ is called an implication. 2. p is called the antecedent.    q is called the consequent. Example: Identify the antecedent and consequent of the following implications. (a) If m = 2, then 2m2 … Read more