What are some examples of logical connectives?

Logical connectives are symbols or words used to combine or modify propositions (statements that can be true or false). They are the building blocks of logical arguments and allow us to form complex statements from simpler ones.

Here are some common examples of logical connectives, along with their symbols and meanings:

1. Conjunction (AND):

* Symbol: ∧

* Meaning: "and"

* Truth Table:

| P | Q | P ∧ Q |

|---|---|-------|

| T | T | T |

| T | F | F |

| F | T | F |

| F | F | F |

* Example: "The sun is shining and the sky is blue."

2. Disjunction (OR):

* Symbol: ∨

* Meaning: "or"

* Truth Table:

| P | Q | P ∨ Q |

|---|---|-------|

| T | T | T |

| T | F | T |

| F | T | T |

| F | F | F |

* Example: "I will eat breakfast or I will have coffee."

3. Negation (NOT):

* Symbol: ¬

* Meaning: "not"

* Truth Table:

| P | ¬P |

|---|---|

| T | F |

| F | T |

* Example: "It is not raining."

4. Conditional (IF...THEN):

* Symbol: →

* Meaning: "if...then"

* Truth Table:

| P | Q | P → Q |

|---|---|-------|

| T | T | T |

| T | F | F |

| F | T | T |

| F | F | T |

* Example: "If you study hard, then you will pass the exam."

5. Biconditional (IF AND ONLY IF):

* Symbol: ↔

* Meaning: "if and only if"

* Truth Table:

| P | Q | P ↔ Q |

|---|---|-------|

| T | T | T |

| T | F | F |

| F | T | F |

| F | F | T |

* Example: "You can go to the party if and only if you are 18 or older."

These are just some of the most common logical connectives. There are other, less common connectives used in advanced logic, like the Sheffer stroke (NAND) and the Peirce arrow (NOR).