Onlinetuition.com SPM Mathematics
4.2c Complement of a Set 1. The complement of set B is the set of all elements in the universal set, ξ, which are not elements of set B, and is denoted by B’. Example 1: If ξ = {17, 18, 19, 20, 21, 22, 23} and B = {17, 20, 21} then B’ = {18, 19, 22, 23} … Read more
4.2b Universal Set 1. Universal set is a set that contains all the elements under consideration. 2. In set notation, the symbol ξ denotes a universal set. Example: Given that the universal set, ξ = {whole numbers less than 9}, A = {prime number} and B = {multiple of 4}. (a) List all the elements of set A and … Read more
4.2a Subsets 1. If every element of a set A is also an element of a set B, then set A is called subset of set B. 2. The symbol ⊂ is used to denote ‘is a subset of’. Therefore, set A is a subset of set B. In set notation, it is written as A ⊂ B. Example: A = {11, … Read more
4.1 Set 1. A set is a collection of objects according to certain characteristics 2. The objects in a set are known as elements. 3. Sets are usually denoted by capital letters and notation used for sets is braces, { }. Example: A = {1, 3, 5, 7, 9} 4. In set notation, the symbol ∈ means ‘is an … 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