Topics are arranged as per SYLLABI published by Maharashtra State Board of Secondary and Higher Secondary Education.
A declarative (assertive) sentence which is either true or false is called statement in logic.
Sentence  Statement or Proposition 

Group of words having some meaning.  Sentence is a statement, if its truth or falsity can be decided. 
Types of Sentences:

Statement has only two values: TRUE : denoted by T FALSE: denoted by F They are denoted by variables, p, q, r, s, etc. Imperative, Interrogative, Exclamatory are not statements. 
Let us consider sentence ; unless we know values of a,b,c and x we cannot say whether statement is true of false. An open sentence is a sentence whole truth can vary according to some conditions which are not stated in the sentence.
An open sentence with a quantifier becomes a statement and is called quantified statements. There are two types of quantifiers:
Conjunction  Disjunction  Negation  Implication / Conditional  Biconditional 

AND (though)  OR  NOT  IF.... THEN  IF AND ONLY IF 
Symbol: ∧  Symbol: ∨  Symbol: ∼  Symbol: or  Symbol: or 
Conjunction of p and q is denoted as p ∧ q  Disjunction of p and q is denoted as p ∨ q  If p is a statement ∼p is read as negation.  p q is read as p implies q  p q is read as p, if and only if q. 
Components p and q are called conjuncts.  Components p and q are called disjuncts  Not used to combine two statements.  p is antecedent and q is consequent.  p and q are called as implicants. 
Binary Connective  Binary Connective  Unary Connective  Binary Connective  Binary Connective 
The truth table of a compound statement shows all the corresponding truth values of the compound statement for all the possible truth values of each prime statement of the compound statement.
A statement pattern is formed by using statements and one or more logic connectives.
Two statements are defined to be logically equivalent if and only if their truth values are identical. Logical equivalence of p and q is expressed as p ≡ q.
Tautology: A statement which is always TRUE.
Contradiction: A statement which is always FALSE. It is also referred as Fallacy.
Contingency: A statement which is neither tautology nor contradiction.
Duality: If A is any statement involving the connectives ∼, ∧, ∨ Then the dual of A is a statement pattern obtained from A by replacing ∧ with ∨ (or by replacing ∨ with ∧). Duel of A is denoted by A^{’}
Negation of compound Statement: is obtained by just inserting 'NOT' at the appropriate place in the statement.
Contrapositive:The statement ∼ q ∼ p is called contrapositive of p q . Here order as well as sign of each prime statement is changed.
Converse: The statement q p is called as the converse of p q. Here order of the prime statement is changed.
Inverse: The statement ∼p ∼ q is called inverse of p q. Sign of each prime statement is changed.
Idempotent law: p ∧ p p
p ∨ p p
Associative law: (p ∨ q) ∨ r = p ∨ (q ∨ r)
(p ∧ q) ∧ r = p ∧ (q ∧ r)
Commutative law: p ∨ q = q ∨ q
p ∧ q = q ∧ p
Distributive law: p ∨ (q ∧ r) = (p ∨ q) ∧ (p ∨ r)
p ∧ (q ∨ r) = (p ∧ q) ∨ (p ∧ r)
Identity law: [The condition that is always true is denoted by T and the condition that is always false is denoted by F]
p ∧ T p
p ∨ F p
Complement Law: ('t' denotes tautology and 'c' denotes contradiction)
p ∨ ∼ p = t
p ∧ ∼ p = c
∼(∼ p) = p
∼t = c
∼c = t
Involution Law: ∼(∼ p) ≡ p
DeMorgan’s laws:
Mathematical Logic has two values either true or false. Similar situation exists in electrical switch. It has two states 'on' (closed) and 'off' (open). Basic series Network and Basic Parallel network serves as building blocks for various types of networks:
Basic Series Network: