Statements
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This document defines and explains different types of statements and logical connectives. It states that a statement is either true or false, and compound statements combine simple statements using connectives like "and", "or", and "if...then". It defines the four main connectives as disjunction, conjunction, implication, and bi-implication. The document also discusses tautologies, contradictions, quantifiers, and the converse, inverse, and contrapositive of an implication statement.
Statements
- 1. STATEMENTS Sentence which is either true or false but not both at the same time is called a statement. Statements are denoted by p,q,r ........ If a statement is true, its truth value is ''T" and if it is false, its truth value is "F" Ex: p: 6 > - 4 (T) If two or more statements combine with the connectives (or, and, if... then, if and only if) are called compound statements. Compound statements are Disjunction, Conjunction, Implication and Bi-implication. If p, q are simple statements p v q (p or q) - Disjunction p q (p and q) - conjunction p q (P implies q) - Implication P q (P double implies q) - Bi-implication Tautologies: Some compound statements contain only 'T' in the last column of their truth tables. Such statements are called tautologies. Ex: p (~q) p Contradiction: A compound statement which contains only "F" in the last column of its truth table is called a contradiction. Ex: p (~p) Quantifiers: 2 types 1) Universal quantifiers 2) Existential quantifier 1) The quantifier, 'for all' or 'for every' denoted by " ", is called the universal quantifier. 2) The quantifier 'for some' or 'there exists atleast one' is called the existential quantifier. It is denoted by " ". Converse, Inverse and Contrapositive of of a Implication: Implication : p q Converse : q p Inverse : ~p ~q Contrapositive : ~q ~p