# In logic, when is a conjunction true?

Jun 27, 2016

A logical conjunction is true if and only if all of its operands are true

#### Explanation:

Here is the Truth table for the conjuction A&B:

{: (underline("| "),underline(" A "),underline(" | "),underline(" B "),underline(" | "),underline(" A&B "),underline(" |")), ("| "," T "," | "," T "," | "," T"," |"), ("| "," T "," | "," F "," | "," F"," |"), ("| "," F "," | "," T "," | "," F"," |"), ("| "," F "," | "," F "," | "," F"," |") :}

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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").