The conjunction of a set of subformulas is true if all of the subformulas are true.
The symbol we use for conjunction is `∧`

.
The conjunction of zero subformulas is trivially true.
The conjunction of a single subformula is equivalent to that subformula.

```
``` A

```
``` A ∧ ~A

```
``` A ∧ B ∧ C

The truth table below shows all possible combinations for a binary conjunction.
Here `t`

stands for true, and `f`

stands for false.

` A ` | ` B ` | ` A ∧ B ` |
---|---|---|

`f` | `f` | `f` |

`f` | `t` | `f` |

`t` | `f` | `f` |

`t` | `t` | `t` |

Doets, Kees. *From Logic to Logic Programming.* MIT Press, 1994.

Copyright © 2014 Barry Watson. All rights reserved.