Connectives and Compound Statement Truth Tables

In this class, We discuss Connectives and Compound Statement Truth Tables.

The reader should have prior knowledge of statements or propositions. Click Here.

We take an example and understand connectives.

Example:

P: I went to school

Q: I played football

P and Q are statements.

In English, and is used as a connective.

I went to school, and I played football.

There is a separate meaning for the connective “and.”

We use “and” when both things happen.

Similarly, connective “or” is used in any of the statements that happened.

Statements formed using connectives are called compound statements.

In our proposition logic, we have connectives and meaning to those connectives

1) Conjunction

2) Dis-junction

3) Negation

Conjunction: Symbol ∧

If both/all the statements are true, then the conjunction is true.

The below diagram shows the truth table for conjunction.

If both p and q are true, then only p ∧ q is true.

Dis-junction: Symbol ∨

If any one of the statements is true, dis-junction is true.

The below diagram shows the dis-junction truth table.

Negation: Symbol ¬

Negation means “not.”

If p is true, negation p is false, and vice versa.

The below diagram shows the truth table.