And-Elimination-Introduction rule - Artificial intelligence:

And-Elimination

In English, this says that "if you know that many things are all true, then you know that any 1 of them is also true". It means that you can make a simple conjunction by just taking 1 of the conjuncts (in effect, eliminating the   s).

A1 ∧  A2 ...∧ An /Ai

Note that 1 ≤ i ≤ n.

And-Introduction

In English language, this says that "if we know that many things are true, then we know that the conjunction of all of them is true", so we may introduce conjunction ('and') symbols.

A1,   A2,  ...,   An/ A1 ∧ A2  ∧ ...  ∧ An

This cannot seem to be saying much. Though, lets that at our knowledge base we are working with very different sentences at different places, and we know some of them are true.  Then we may make a bigger sentence out of them by conjoining the smaller ones.