PART A What is truth table? A truth table is a table that displays the relationships between the truth values of propositions and that of compound proposition constructed from them. The truth table for the disjunction of two p and q p q pΛq T T T T F F F T F F F F Define conjunction? When p and q are any two propositions, the proposition and q” denoted by p q “p Λ and called the conjunction of p and q is defined as the compound proposition that is true when both p and q are true and is always false otherwise. Define disjunction? When p and q are any two propositions, the proposition or q” denotd by p V q and “p called the conjunction of p and q is defined as the compound proposition that is false when both p and q are false and is always true otherwise. What is the order of precedence for logical connectives? The orders of precedence for the logical connectives are The negation operator has precedence over all other logical operators. Thus ~p q (~p) q, not ~ (p q). Λ Λ Λ The conjunction operator has precedence over the disjunction operator. Thus p q V r means (p q) V r, but not p (q V r). Λ Λ Λ The conditional and bi-conditional operator’s and have lower → ↔ precedence than other operators. Among them, has precedence over → ↔. Define conditional proposition? If p and q are propositions, the compound proposition p, then q”, that is denoted by p “if q is called a conditional proposition, which is false when p is true and q is false and → true otherwise. Define tautology and contradiction? A compound proposition P = P (p1, p2,- - - - - - - pn) where p1, p2, . . . . . , pn are variables (elementary propositions), is called tautology, if it is true for every truth assignment for p1, p2, pn. P is called contradiction, if it is false for every truth … …, assignment for p1, p2, pn … …., Define duality law?
PART A What is truth table? A truth table is a table that displays the relationships between the truth values of and that of compound proposition constructed from them. The truth table for the disjunction of two propositions p and q p q pΛq T T T T F F F T F F F F Define conjunction? When p and q are any two propositions, the proposition “p and q” denoted by p Λ q and called the conjunction of p and q is defined as the compound proposition that is true when both p and q are true and is always false otherwise. Define disjunction? When p and q are any two propositions, the proposition “p or q” denotd by p V q and called the conjunction of p and q is defined as the compound proposition that is false when both p and q are false and is always true otherwise. What is the order of precedence for logical connectives? The orders of precedence for the logical connectives are The negation operator has precedence over all other logical operators. Thus ~p Λ q (~p) Λ q, not ~ (p Λ q). The conjunction operator has precedence over the disjunction operator. Thus p Λ q V r means (p Λ q) V r, but not p Λ (q V r). The conditional and bi-conditional operator’s → and ↔ have lower precedence than other operators. Among them, → has precedence over ↔. Define conditional proposition? If p and q are propositions, the compound proposition “if p, then q”, that is denoted by p → q is called a conditional proposition, which is false when p is true and q is false and true otherwise. Define tautology and contradiction? A compound proposition P = P (p1, p2,- - - - - - - pn) where p1, p2, . . . . . , pn are variables (elementary propositions), is called tautology, if it is true for every truth assignment for p1, p2, … …, pn. P is called contradiction, if it is false for every truth assignment for p1, p2, … …., pn Define duality law?
unit-2-part-a.docx