##### Basics of Propositional Logic | Operators on propositions | Negation | Conjunction | Disjunction | Conditional Statements

**Proposition**: A declarative statement that can be either True or False but not both.

**Operators on propositions:
1. Negation(¬):** ¬p is the opposite of the truth value of p.

**2. Conjunction(∧):**p∧q will be true iff both p and q are true. You can think this as '

**AND**'.

**3.**

**Disjunction(∨):**p∨q will be false iff both p and q are false. You can think this as '

**OR**'.

**Incusive 'OR' statement:**Students who have taken Calculus or Algebra can take this class.**Exclusive 'OR' statement:**Students who have taken Calculus or Algebra, but not both can take this class.**Conditional Statements:**

**1**.

**if p then q**(p→q) : Here p is premise or hypothesis and q is conclusion or consequence. The conditional statement p→q is false when p is true and q is false.

Example:

p: Rohan learns programming.

q: Rohan will find a good job.

We can express p→q in different ways :

p→q : If Rohan learns programming, then he will find a good job.

p→q : Rohan will find a good job unless he does not learn programming.

p→q: Rohan will fine a good job when he leans programming

**2**.

**p if and only if q**(p↔q) : The biconditional statement p↔q is true when p and q have the same truth values, and false otherwise.

Example:

p: You can take flight.

q: You buy a ticket.

p↔q : You can take flight if and only if you buy a ticket.