Building Security System A new building is creating
Building Security System A new building is creating a security system with three alarm types. A flood alarm, a fire alarm and an intrusion alarm. Whenever the intrusion or fire alarm goes off, the police department is called. Whenever the fire or flood alarm goes off the fire department is called. But, if the flood alarm goes the police department is NOT called. . Similarly, if the intrusion alarm goes off the fire department is not alerted. A = intrusion alarm B = flood alarm C = fire alarm If intrusion OR fire alarm call police If fire OR flood alarm call fire department If flood NOT police If intrusion NOT fire Copyright © 2009 by Helene G. Kershner
Building Security System • Under what conditions would A (intrusion alarm) go off? • Under what conditions would B (flood alarm) go off? • Under what conditions would C (fire alarm) go off? • Under what conditions are the fire department called? • Under what conditions are the police called? Copyright © 2009 by Helene G. Kershner
Building Security System A = Intrusion Alarm If only A goes off, who is called? A If only B goes off, who is called? If only C goes off, who is called? B B = Flood Alarm C C = Fire Alarm Copyright © 2009 by Helene G. Kershner
Building Security System A = intrusion alarm B = flood alarm C = fire alarm Police called If intrusion OR fire alarm Police = A OR C = A+C P = A+C Fire department called If fire OR flood alarm Fire Dept. = B OR C = B+C F = B+C If flood NOT police B = ~P = F If intrusion NOT fire A = ~F = P Copyright © 2009 by Helene G. Kershner
Building Security System Intrusion alarm = A, Flood alarm = B, Fire alarm = C Police or A 0 0 1 1 B 0 0 1 1 C 0 1 0 1 Fire Dept. or (any row with a 1 1) A+C B+C Copyright © 2008 by Helene G. Kershner
Building Security System Intrusion alarm = A, Flood alarm = B, Fire alarm = C Police OR A 0 0 1 1 B 0 0 1 1 Fire Dept. OR (any row with a 1 1) C A+C B+C 0 0 1 1 1 Copyright © 2008 by Helene G. Kershner
Building Security System Intrusion alarm = A, Flood alarm = B, Fire alarm = C Police or A 0 0 1 1 B 0 0 1 1 Fire Dept. or (any row with a 1 1) C A+C B+C 0 0 0 1 1 1 1 0 1 1 1 Copyright © 2008 by Helene G. Kershner
Building Security System Intrusion alarm = A, Flood alarm = B, Fire alarm = C Remember: A+C = Police, B+C = Fire A 0 0 1 1 B 0 0 1 1 C A+C B+C 0 0 0 1 1 1 1 0 1 1 1 Now lets ask some questions: 1) If an intruder enters the building, which alarm goes off? A=1, B=0, C=0 Copyright © 2008 by Helene G. Kershner
Building Security System Intrusion alarm = A, Flood alarm = B, Fire alarm = C Remember: A+C = Police, B+C = Fire A 0 0 1 1 B 0 0 1 1 C A+C B+C 0 0 0 1 1 1 1 0 1 1 1 Now lets ask some questions: 1) If an intruder enters the building, which alarm goes off? A=1, B=0, C=0 2) If the building is empty and a fire starts and sets off the sprinkler system, who gets called? A=0, B=1, C=1 Copyright © 2008 by Helene G. Kershner
Building Security System Intrusion alarm = A, Flood alarm = B, Fire alarm = C Remember: A+C = Police, B+C = Fire A 0 0 1 1 B 0 0 1 1 C A+C B+C 0 0 0 1 1 1 1 0 1 1 1 Now lets ask some questions: 1) If an intruder enters the building, which alarm goes off? A=1, B=0, C=0 2) If the building is empty and a fire starts and sets off the sprinkler system, who gets called? A=0, B=1, C=1 3) If an intruder sets a fire to cover his tracks, who get called? A=1, B=1, C=0 Copyright © 2008 by Helene G. Kershner
Logic – Order of Operations • In Logic as in basic arithmetic the operations are ordered based on their importance 1. Parenthesis (these say DO ME FIRST) 2. NOT (~) 3. AND (۰ ) 4. OR (+) Copyright © 2008 by Helene G. Kershner
Solving Logic Problems Solve the following: R = ~(A+B)B Read as R = NOT (A OR B) AND A 1. Create Truth Table with 2 columns 2. Solve (A+B) 3. Solve ~(A+B) 4. Solve entire equation ~(A+B)B What is R, when A = 1, B = 0 A 0 0 1 1 B (A+B) ~(A+B)A 0 1 Copyright © 2009 by Helene G. Kershner
Solving Logic Problems Solve the following: R = ~(A+B)B Read as R = NOT (A OR B) AND A 1. Create Truth Table with 2 columns 2. Solve (A+B) 3. Solve ~(A+B) 4. Solve entire equation ~(A+B)B What is R, when A = 1, B = 0 A 0 0 1 1 B (A+B) ~(A+B)A 0 0 1 1 1 Copyright © 2009 by Helene G. Kershner
Solving Logic Problems Solve the following: R = ~(A+B)A Read as R = NOT (A OR B) AND A 1. Create Truth Table with 2 columns 2. Solve (A+B) 3. Solve ~(A+B) 4. Solve entire equation ~(A+B)B What is R, when A = 1, B = 0 A 0 0 1 1 B (A+B) ~(A+B)A 0 0 1 1 1 0 0 1 1 0 Copyright © 2009 by Helene G. Kershner
Solving Logic Problems Solve the following: R = ~(A+B)A Read as R = NOT (A OR B) AND A 1. Create Truth Table with 2 columns 2. Solve (A+B) 3. Solve ~(A+B) 4. Solve entire equation A 0 0 1 1 B (A+B) ~(A+B)A 0 0 1 1 0 0 What is R, when A = 1, B = 0 ? R=0 Copyright © 2009 by Helene G. Kershner
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