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Not (A and B) is the same as Not A and Not B.Group startsTrue or FalseTrue, unselectedFalse, unselected

Question

Not (A and B) is the same as Not A and Not B.Group startsTrue or FalseTrue, unselectedFalse, unselected

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Solution

To answer the question, let's break it down step by step:

  1. The statement "Not (A and B)" is equivalent to "Not A or Not B" according to De Morgan's laws.

  2. The statement "Not A and Not B" means that both A and B are false.

  3. In the given group, we have two options: True or False for A, and True or False for B.

  4. If A is True and B is True, then "Not A and Not B" would be False and the statement "Not (A and B)" would also be False.

  5. If A is True and B is False, then "Not A and Not B" would be False and the statement "Not (A and B)" would also be False.

  6. If A is False and B is True, then "Not A and Not B" would be False and the statement "Not (A and B)" would also be False.

  7. If A is False and B is False, then "Not A and Not B" would be True and the statement "Not (A and B)" would also be True.

Therefore, the statement "Not (A and B)" is not always the same as "Not A and Not B". It is only equivalent when both A and B are False.

This problem has been solved

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