‘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.

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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.

‘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.

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Question ID: mtid-5-stid-8-sqid-4018-qpid-2717