The truth or the falsehood of the propositions obtained in this way depend on the truth or falsehood of the initial propositions and on a corresponding treatment of the connectives as operations on propositions. Often truth is symbolized by the digit "1" and falsehood by the digit "0" . The connectives "and" , "or" , "if … then" , and "is equivalent to" are denoted, respectively, by the symbols & (conjunction), (disjunction), (implication)