Correct option is D
The given Boolean expression is
(A · B)', which is the negation (NOT) of the AND operation between
A and
B. According to
De Morgan's Law, the negation of an AND operation is equivalent to the OR operation of the negations of the individual variables.
De Morgan's Law states:
(A⋅B)′ = A′ + B′
So,
(A · B)' is equivalent to
A' + B'.
Important Key Points:
1.
De Morgan's Law: This law is a fundamental rule in Boolean algebra that allows you to simplify expressions involving NOT, AND, and OR.
·
(A · B)' = A' + B'
·
(A + B)' = A' · B'
2.
Negation of AND: When you negate an AND operation, the result is the OR of the negations of the operands.
Knowledge Booster:
·
Option (a):
A' · B' is the incorrect result. This would be the result if we applied
De Morgan's law to
(A + B)' (NOT OR).
·
Option (b):
A + B' is incorrect. This expression does not match the result of negating the AND of
A and
B.
·
Option (c):
A · B' is incorrect. This is just a simple combination of
A and
B', not a result of negating an AND operation.
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