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 $A$