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

Example 1: Form a compound statement by combining two given statements using the word ‘and’. (a) 3 × 12 = 36  7 × 5 = 35 (b) 5 is a prime number.  5 is an odd number. (c) Rectangles have 4 sides.  Rectangles have 4 vertices. Solution: (a) 3 × 12 = 36 and 7 × 5 = 35 (b) 5 is a … Read more

3.3 Operations on Statements   (A) Nagating a Statement using ‘No’ or ‘Not’   1. Negation of a statement refers to changing the truth value of the statement, that is, changing a true statement to a false statement and vice versa, using the word ‘not’ or ‘no’.   Example 1: Change the true value of the following … Read more

Example 1: Complete each of the following statements using the quantifiers ‘all’ or ‘some’ to make the statement true. (a) _____ rectangles are squares. (b) _____ prime numbers are odd numbers. (c) _____ triangles have equal sides. (d) _____ even numbers are divisible by 2. Answer: (a) Some rectangles are squares. (b) Some prime numbers … Read more

3.2 Quantifiers ‘All’ and ‘Some’   Statement using ‘All’ and ‘Some’ 1. Quantifiers are words that denote the number of objects or cases referred to in a given statement. 2. Quantifier ‘all’, ‘any’ and ‘every’ describe each and every object or case. 3. Quantifier ‘some’, ‘several’ and ‘part of’ describe one or more objects or cases.   Example: Complete each … Read more

Example 1: Determine whether the following sentences are statements or not. Give a reason for your answer. (a) 3 + 3 = 8 (b) 9 – 4 = 5 (c) A pentagon has 5 sides. (d) 4 is a prime number. (e) Is 40 divisible by 3? (f) Find the perimeter of a square with … Read more

(A) Determine Whether a Given Sentence is a Statement 1. A statement is a sentence which is either true or false but not both. 2. Sentences which are questions, instructions and exclamations are not statements. Example 1: Determine whether the following sentences are statements or not. Give a reason for your answer. (a) 3 + 3 … Read more