Propositional Logic

Step 1: Identifying the Switches and Logic Representation
The given circuit consists of switches , arranged in both series and parallel configurations. - Switches and are controlled by input . - Switches and are controlled by input .
Step 2: Deriving the Boolean Expression
- The parallel arrangement corresponds to the logical OR operation. - The series arrangement corresponds to the logical AND operation. Hence, the Boolean expression for the circuit is:
Step 3: Constructing the Truth Table

Step 1: Understanding Logical Operators
- means "If , then ".
- represents logical AND.
- represents logical implication.
Step 2: Constructing the Truth Table

Step 1: Understanding the Concept of Duality
Duality in logic involves the following transformations:
- Replacing (OR) with (AND), and vice versa.
- Swapping with , and vice versa.
Step 2: Applying Duality to the Given Expression
For the expression , applying the duality principle gives: Hence, the correct result is .