Compound statements and truth tables

Summary

If \(A\) and \(B\) are two predicates, then the following are statements

• “If \(A\) , then \(B\) ” or “ \(A \implies B\) ”
• “If \(B\) , then \(A\) ” or “ \(B \implies A\) ”, the converse of “ \(A \implies B\) ”
• “ \(A\) if and only if \(B\) ” or “ \(A \iff B\) ” , the equivalence of \(A\) and \(B\)
• “ \(A\) and \(B\) ” , the conjunction of \(A\) and \(B\)
• “ \(A\) or \(B\) ” , the disjunction of \(A\) and \(B\)
• “Not \(A\) ”, the negation of \(A\)