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Question 200 of 227

Q.Construct the switching circuit for the statement (p∧q)∨(∼p)∨(p∧∼q)(p \land q) \lor (\sim p) \lor (p \land \sim q).

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2017Subjective· 3mImportance★★★★★
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Figure — Draw a switching circuit with two terminals (input and output, with the lamp L at the output). Betwe
Figure — Draw a switching circuit with two terminals (input and output, with the lamp L at the output). Betwe

Each conjunction (∧\land) is a series connection of switches; each disjunction (∨\lor) is a parallel connection of branches.

The statement pattern is (p∧q)∨(∼p)∨(p∧∼q)(p\land q)\lor(\sim p)\lor(p\land\sim q), a disjunction of three terms, so the circuit has three branches in parallel between the input and output terminals:

  • Branch 1: switch pp in series with switch qq (represents p∧qp\land q)
  • Branch 2: switch ∼p\sim p alone (represents ∼p\sim p)
  • Branch 3: switch pp in series with switch ∼q\sim q (represents p∧∼qp\land\sim q) …
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