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Exercise 1.5 · Q119

Q.Construct the switching circuit of the following: (∼p∧q)∨(p∧∼r)(\sim p \wedge q) \vee (p \wedge \sim r)

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In switching-circuit theory, conjunction (∧\wedge) corresponds to two switches placed in SERIES (current flows only when both are closed), and disjunction (∨\vee) corresponds to two branches placed in PARALLEL (current flows if either branch is closed).

The expression is (∼p∧q)∨(p∧∼r)(\sim p \wedge q) \vee (p \wedge \sim r), a disjunction of two conjunctions, so it becomes two branches in parallel:

  • Branch 1: switch ∼p\sim p in series with switch qq.
  • Branch 2: switch pp in series with switch ∼r\sim r. …

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