logical Operators:

Logical Operator:

In logic, logical operators are symbols or words used to connect propositions and form new statements. Propositions are always denoted by small letters such as p, q, r.

1. Conjunction (AND)

A conjunction connects two propositions with AND ( ∧ ).
The compound statement is true only if both propositions are true.

Symbol:
𝑝∧𝑞
Example:
p: Today is Friday
q: It is raining

p ∧ q: Today is Friday and it is raining

2. Disjunction (OR)

A disjunction connects two propositions with OR ( ∨ ).
The compound statement is true if at least one proposition is true.

Symbol:
𝑝∨𝑞
Example:

p: Today is Friday

q: It is raining

p ∨ q: Today is Friday or it is raining

3. Negation (NOT)

A negation reverses the truth value of a proposition.
If a proposition is true, its negation is false, and vice versa.

Symbol:
¬𝑝
Example:

p: Today is Friday

¬p: Today is not Friday

4. Implication (IF…THEN)

An implication shows a conditional relationship: if p then q.
It is false only if p is true and q is false; otherwise true.

Symbol:
𝑝→𝑞
Example:

p: It is raining

q: The ground is wet

p → q: If it is raining, then the ground is wet

5. Biconditional (IF AND ONLY IF)

A biconditional statement is true if both propositions have the same truth value.
It is read as p if and only if q.

Symbol:
𝑝↔𝑞

Example:

p: I will go to the park

q: It is sunny

p ↔ q: I will go to the park if and only if it is sunny

✅ Note: Logical operators are the building blocks for creating compound propositions in logic.