1. Atomic proposition: These are the simple propositions; it consists of a single proposition symbol. These are the sentences which must be either true or False. For example: 2+2 is 4, is an atomic proposition and it is True. 2+2 is 5, is an atomic proposition but it is False.

2. Compound proposition: Compound propositions are the combination of two or more Atomic-propositions using parenthesis and logical connectives. For example: it is raining today and the street is wet. Here “and” is the logical connective which connects these 2 statements.

1. Negation: A sentence such as ¬P is called the negation of P. Negation of a statement makes its meaning opposite of original statement.

2. Conjunction: A sentence having ∧ connective such as P ∧ Q is called a conjunction operator. Which is used like AND. For example,
P: John is intelligent.
Q: John is hardworking.
p ∧ q: John is intelligent and hardworking.

3. Disjunction: A sentence having ∨ connective such as P ∨ Q is called a disjunction operator. Which is used like OR. For example,
P: John is a doctor.
Q: John is an engineer.
p ∨ q: John is a doctor or an engineer.

4. Implication: Implications are like if – then rules, for example,
P: It is raining today
Q: The street is wet
P → Q: If it is raining today, then the street is wet.

5. Biconditional: A sentence which is like P ⇔ Q i.e., it is similar to implication but bidirectionally. For example,
P: He is breathing.
Q: He is alive
P ⇔ Q: If he is breathing then he is alive.