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The negation of the statement "Amit lives in Delhi and Aman does not live in Mumbai" is

  • A.Amit lives in Delhi and Aman lives in Mumbai
  • B.Amit does not live in Delhi and Aman lives in Mumbai
  • C.Amit does not live in Delhi or Aman does not live in Mumbai
  • D.Amit does not live in Delhi or Aman lives in Mumbai

Answer: D

The negation is Amit does not live in Delhi or Aman lives in Mumbai.

The statement has the form 'p and not q', where p is 'Amit lives in Delhi' and q is 'Aman lives in Mumbai'. By De Morgan's law the negation of 'p and not q' is 'not p or q'.

So the 'and' becomes 'or', the first part is negated, and the second part loses its 'not': Amit does not live in Delhi, or Aman lives in Mumbai.

The options keeping 'and' fail because negation swaps 'and' for 'or'. The option with 'Aman does not live in Mumbai' forgot to negate the second part.

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