Answer to Question #103628 in Discrete Mathematics for na

Question

‘A is sufficient for B’ is equivalent to ‘the negative of A is necessary for the
negative of B’. Is it true or false? give reasons.

Answer 1

Definition: A condition $A$ is said to be sufficient for a condition $B,$ if (and only if) the truth (/existence /occurrence) of $A$ guarantees (or brings about) the truth (/existence /occurrence) of $B.$

Definition: A condition $A$ is said to be necessary for a condition $B,$ if (and only if) the falsity (/nonexistence /non-occurrence) of $A$ guarantees (or brings about) the falsity (/nonexistence /non-occurrence) of $B.$

$A$ is a sufficient condition of $B=df$  the absence of $A$ is a necessary condition of the absence of $B.$

$B$ is a necessary condition of $A=df$ the absence of $B$ is a sufficient condition of the absence of $A.$

$'A$ is sufficient for $B'$ is equivalent to $'$ the negative of $A$ is necessary for the negative of $B'.$ True.