Statements & Sets
Statement:
A sentence which is either true or false but not both is called "statement".
♦ Truthfulness of a statement is denoted by 'T' whereas it's falsity is denoted by 'F'.
♦ Statements are denoted by lower case alphabets of English like p, q, r, s…etc.
♦ Statements are denoted by lower case alphabets of English like p, q, r, s…etc.
Open Sentence: A sentence which is not a statement is called "open sentence". (or) A
mathematical sentence which has atleast one variable is called "open sentence".Eg: 1. p : 2 × 5 = 7 is a false statement.
2. q : 2 is even prime is a true statement.
3. r : x + y = 8 is an open sentence but not statement.
Connectives: The words that are used to combine the simple statements are called
connectives.
Eg: and, or, if then, if and only if, not... etc.
Compound Statements: The statements that are composed of other simple statements
with the connectives are called "compound statements".
Negation: If 'p' is a statement, then negation of p is denoted by "∼p" and it is formed by
using the word 'not' before 'p', read as "negation p".
Conjunction: The compound statement that is combined two simple statements with the
connective "AND" is called "Conjunction".
-->The symbol of conjunction is ''∧''read as "and".
Disjunction: The compound statement that is combined two simple statements with the
connective "OR" is called "Disjunction".
Conditional or Implication: The compound statement that is combined two simple
statements with the connective "if-then" is called "conditional".
--> The symbol of conditional is "→" or "⇒" read as "if-then" or "implies".
Biconditional or Bi-implication: The compound statement that is combined two simple
statements with the connective "IF AND ONLY IF" or "IFF" is called bi-conditional.
--> The symbol of bi-conditional is "↔" or "⇔" read as if and only if or briefly "if".
Conditional : p ⇒ q
Converse : q ⇒ p
Inverse : (∼p) ⇒ (∼q)
Contrapositive : (∼q) ⇒ (∼p)
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