(i)
Straight forward approach It is a chain of arguments which leads directly from
what is given or assumed,  with the help of axioms, definitions or already proved
theorems, to what is to be proved using rules of logic Consider the following example:
Example 1 Show that if x2 – 5x + 6 = 0, then x = 3 or x = 2 Solution x2 – 5x + 6 = 0 (given)
Appendix 1
PROOFS IN MATHEMATICS
Rationalised 2023-24
 MATHEMATICS
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⇒ (x – 3) (x – 2) = 0 (replacing an expression by an equal/equivalent expression)
⇒ x – 3 = 0 or x – 2 = 0 (from the established theorem ab = 0 ⇒ either a = 0 or
b = 0, for a, b in R)
⇒ x – 3 + 3 = 0 + 3 or  x – 2 + 2 = 0 + 2 (adding equal quantities on either side of the
equation does not alter the nature of the
equation)
⇒ x + 0 = 3 or x + 0 = 2  (using the identity property of integers under addition)
⇒ x = 3 or x = 2 (using the identity property of integers under addition)
Hence, x2 – 5x + 6 = 0 implies x = 3 or x = 2 Explanation Let p be the given statement “x2 – 5x + 6 = 0” and q be the conclusion
statement “x = 3 or x = 2”