Final Answer:
The simplified Boolean expression for the given logic diagram is ( F = A'B + AB' + AC ).
Explanation:
The logic diagram provided corresponds to a combination of AND, OR, and NOT gates. The expression, ( F = A'B + AB' + AC ), captures the logic depicted in the diagram. This Boolean expression signifies that the output ( F ) is true if either A and B are false while A and C are true, or if A is true and ( B ) is false, regardless of( C \)'s value.
The simplified expression is obtained through the application of Boolean algebra rules. Firstly, examining the output of each gate in the diagram and then writing the expressions for their corresponding outputs. Next, employing the rules of Boolean algebra such as De Morgan's theorem, distribution, and complement laws, to simplify the combined expression into a more compact form. Through this process, the expression ( F = A'B + AB' + AC ) is derived, which represents the logical behavior of the given circuit in a minimized form.
This simplified expression helps in reducing the complexity of the circuit, making it easier to analyze and implement. It provides a clear understanding of the relationships between the input variables and the resulting output in the logic circuit, aiding in efficient circuit design and troubleshooting.
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