3.7 Switching Circuits 165 Warm Up Exercises In Exercises 1– 4, fill in the blanks with an appropriate word, phrase, or symbol(s). 1. A conjunction, ,∧ is used to represent switches in a(n) _________ circuit. Series 2. A disjunction, ,∨ is used to represent switches in a(n) _________ circuit. Parallel 3. When a switch labeled as p is open, a switch labeled as p is _________. Closed 4. Two circuits are equivalent if they have equivalent _________ statements. Symbolic Practice the Skills/Problem Solving In Exercises 5–12, (a) write a symbolic statement that represents the circuit and (b) construct a truth table to determine when the lightbulb will be on. That is, determine which switches must be open and which switches must be closed for the lightbulb to be on. 5. p q * 6. p q * 7. p q q * 8. p q p q * 9. p p q r q * 10. p q p r q * 11. r p q p * 12. p q q p p q * In Exercises 13–20, draw a switching circuit that represents the symbolic statement. 13. p q r ( ) ∨ ∧ * 14. p q r ( ) ∨ ∧ * 15. p q r (~ ~ ) ∨ ∧ * 16. p q r ( ) ∼ ∧ ∨ * 17. p q r s ( ) ( ) ∨ ∧ ∨ * 18. p q r s ( ) ( ) ∧ ∨ ∧ * 19. p q r q p ( ) ( ) ( ) [ ] ∨ ∨ ∧ ∧ ∼ * 20. p q r p q ( ) ( ) [ ] ∨ ∧ ∨ ∼ ∧ * In Exercises 21–26, represent each circuit with a symbolic statement. Then use a truth table to determine if the circuits are equivalent. 21. p , p q q p q p q ; ; ∨∼ ∼ ∧ not equivalent 22. q q q p p q , ∧ ∼ ∨ ∨ ∧ ∼ p q q p q q ( ) ; ( ) ; not equivalent 23. p q r q r p p , ∧ ∨ ∧ ∨ ∧ p q r p q r p [( ) ] ; ( ) ; equivalent 24. p q r p q r p , p q r p q p r ( ); ( ) ( ); ∧ ∨ ∧ ∨ ∧ equivalent *See Instructor Answer Appendix SECTION 3.7 Exercises
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