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What are the 5 basic logic connectives?
- Authors
- Name
- Lucas Rosvall
- @lucasrosvall
The five basic logic connectives are negation, conjunction, disjunction, implication and equivalence.
In this article we will dive deeper into what this means and how these connectives are used in logic.
The 5 basic logic connectives
There are 5 connectives that are used in logic, and they are negation, conjunction, disjunction, implication and equivalence.
Below you can find a table what these connectives means, where P and Q are statements.
| Statement | Connectives | Sympolic form | Type of statement |
|---|---|---|---|
| Not P | Not | ~P | Negation |
| P and Q | And | P ^ Q | Conjunction |
| P or Q | Or | P v Q | Disjunction |
| If P, then Q | If…, then… | P ⇒ Q | Conditional |
| P if and only if Q | If.. and only if.. | P ↔ Q | Biconditional |
These logical connectivies is often used to build complex statements out of simplier statements such as Not Q or If P, then Q.
A statement is an expression which can be either true or false.
How are connectives used in Logic?
As said above, logical connectivies is often used to build statements out of simplier statements.
However, logical connectivies is also often used together with a truth table which shows all possible combinations of a given statement.
Truth tables
Logical connectives can be used for a truth table, which is a table showing the truth value (either “T” if True, and “F” if False) for all of the possible combinations of a given statement.
You can find a simple truth table below as an example.
| P | Q | P ^ Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Since P ^ Q means P and Q, this statement will only be true when both P and Q are true which can can see above.
Summary
This was a short article about the five basic logic connectives are negation, conjunction, disjunction, implication and equivalence. They are used to build statements out of simplier statements.