Mathematical Foundation of Computer Science

DHARM 104 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE The sentences 1, 2, 3, 4 and 5 are statements that have assigned the truth ...

DHARM PROPOSITIONAL LOGIC 105 Take another example, Statement (1) : Stuart is an efficient driver (symbolic logic) K Statement ( ...

DHARM 106 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE Consider another example, ‘I will take the meal “or” I will go’. Here sens ...

DHARM PROPOSITIONAL LOGIC 107 Write the statement in symbolic form. (i) If it rains but I stay home. I won’t be wet. Given state ...

DHARM 108 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE and negation (~). Other connectors like implication (→), equivalence (⇔) t ...

DHARM PROPOSITIONAL LOGIC 109 (iv) Here, the LHS formula (A ↔ B), which read as “A if and only if B” is called a biconditional f ...

DHARM 110 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE AB⊗ 1 ⊗ 2 ⊗ 3 ⊗ 4 ⊗ 5 ⊗ 6 ⊗ 7 ⊗ 8 ⊗ 9 ⊗ 10 ⊗ 11 ⊗ 12 ⊗ 13 ⊗ 14 ⊗ 15 ⊗ 16 F ...

DHARM PROPOSITIONAL LOGIC 111 5.4.4 Formation Tree of a Formula................................................................. ...

DHARM 112 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE Consider the formation tree shown in Fig. 5.13. Determine the truth value ...

DHARM PROPOSITIONAL LOGIC 113 · The formula (X ∨Y) can get value F under ‘v’ if and only if both X and Y get value F under ‘v’. ...

DHARM 114 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE 5.5 Tautology............................................................. ...

DHARM PROPOSITIONAL LOGIC 115 R F F T T C F* T F* T RC→ T T F T Corresponding to above, symbolic logic of two premises & con ...

DHARM 116 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE In the next sections we will discuss several methods to test the validity ...

DHARM PROPOSITIONAL LOGIC 117 Now construct the truth table for X, we observe that formula X is not a tautology. There- fore, ar ...

DHARM 118 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE Thus, for following truthvalues, argument is invalid, A:T B:F C : ......(T ...

DHARM PROPOSITIONAL LOGIC 119 and construct the truth table for X. From Fig. 5.23 we find that formula X is a tautology, therefo ...

DHARM 120 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE Rule 3. Hypothetical Syllogism (HP) Rule 4. Disjunctive Syllogism (DS) (i) ...

DHARM PROPOSITIONAL LOGIC 121 Example 5.15. Show conclusion E follows logically from given premises: A → B, B → C, C → D, ~ D an ...

DHARM 122 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE to solve the problem. Hence, we have another 10 rules. These rules are cal ...

DHARM PROPOSITIONAL LOGIC 123 Example 5.18. J ∨ (~ K ∨ J) K ∨ (~ J ∧ K) / ∴ (J ∧ K) ∨ (~ J ∧ ~ K) (Apply rules of inference and ...