In logic, when is a conjunction true?
A logical conjunction is true if and only if all of its operands are true
Here is the Truth table for the conjuction A&B:
You should realize that the term conjunction has a slightly different meaning when applied to general English grammar.
In English grammar, a conjunction is simply a word that connects two independent clauses to form a single sentence.
For example, in the sentence:
You must hurry or we will be late.
"or" is considered a conjunction in English grammar;
but it is not a conjunction in terms of logic or mathematics (in those situations it is called a "disjunction").