# Logical Operations And Logical Connectivity

**LOGICAL OPERATIONS OR LOGICAL CONNECTIVES :** The phrases or words which combine simple statements are called logical connectives.

**For example,** ‘and’, ‘or’, ‘note’, ‘if……then’, ‘either…….or’ etc…. In the following table we list some possible connectives, their symbols & the nature of the compound statement formed by them.

Now we shall study each of basic logical connectives in details.

**Basic Logical Connectives :**

**Conjunction (AND) :** If two statements are combined by the word “and” to form a compound proposition (statement) is called the conjunction of the original

proposition. Symbolically, if P & Q are two simple statements, then ‘ P ∧Q ’ denotes the conjunction of P and Q and is read as ‘P and Q.

Since, P ∧Q is a proposition it has a truth value and this truth value depends only on the truth values of P and Q.

Specifically, if P & Q are true then P ∧Q is true; otherwise P ∧Q is false.

The truth table for conjunction is as follows.

**Example 3 :**

Let P : Monsoon is very good this year.

Q : The rivers are rising.

then P ∧Q : Monsoon is very good this year and rivers are rising.

**Disjunction (OR) :** Any two statements can be connected by the word ‘or’ to form a compound statement called disjunction.

Symbolically, if P and Q are two simple statements, then P ∧Q denotes the disjunction of P and Q and read as 'P or Q' .

The truth value of P ∧Q depends only on the truth values of P and Q. specifically if P and Q are false then P ∧ Q is false otherwise P ∧Q is true.

The truth table for disjunction is as follows.

Example 4 :

P : Paris is in France

Q : 2 3 = 6

then P ∨Q : Paris is in France or 2 3 = 6. Here, P ∨Q is True since P is true & Q is False. Thus, the disjunction P ∨Q is false only when P and Q are both false.