Title Mathematical Reasoning - 5.pptx ✅

MATHEMATICAL REASONING Validating Statements General rules for checking whether a given compound statement is true or not. Rule 1. Statements with ‘And’: Let p and q be two statements. Then, in order to prove that ‘p and q’ is true, the following steps are taken. Step 1. Show that p is true. Step 2. Show that q is true. Rule 2. Statements with ‘or’: Let p and q be two statements. Then, in order to prove that ‘p or q’ is true, we proceed as under. Case 1. Assume that p is false and show that q is true. Case 2. Assume that q is false and show that p is true.
MATHEMATICAL REASONING Rule 3. Statements with ‘If .... then’: Let p and q be two statements. Then, in order to prove that ‘p ⇒ q’ is true, we need to prove any one of the following. DIRECT METHOD Assume that p is true and prove that q is true. CONTRAPOSITIVE METHOD Assume that q is false and prove that p is false. Rule 4. Statements with ‘If and only if ’: In order to prove that ‘p ⇒ q’, we need to show that: (i) If p is true, then q is true. (ii) If q is true, then p is true.