A is sufficient for B can be written as A→B ---(1)
The negative of A is necessary for the negative of B can be written as ¬B→¬A ---(2)(2)⟹¬B→¬A⟺¬(¬B)∨¬A
⟺¬(¬B∧A) (Using DeMorgan's laws)
⟺¬(¬(¬(¬B∧A))) (As A⟺¬¬A )
⟺¬(¬B∧A) (As ¬¬A⟺A )
⟺B∨¬A⟺¬A∨B (Using DeMorgan's laws)
⟺A→B⟺(1)
Thus, (2) is equivalent to (1).
Hence, the statement 'A is sufficient for B’ is equivalent to ‘the negative of A is necessary for the
negative of B’ is TRUE.
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