Ee20-hw2-s08-sol - EECS 20N Structure and Interpretation of Signals and Systems Department of Electrical Engineering and Computer Sciences

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Unformatted text preview: EECS 20N: Structure and Interpretation of Signals and Systems Department of Electrical Engineering and Computer Sciences UNIVERSITY OF CALIFORNIA BERKELEY Problem Set 2 SOLUTIONS HW 2.1 (a) DeMorgan’s Laws P Q ¬ ( P ∧ Q ) ¬ P ∨ ¬ Q T T F F T F T T F T T T F F T T P Q ¬ ( P ∨ Q ) ¬ P ∧ ¬ Q T T F F T F F F F T F F F F T T (b) Distributive Laws P Q R Q ∨ R P ∧ ( Q ∨ R ) T T T T T T T F T T T F T T T T F F F F F T T T F F T F T F F F T T F F F F F F P Q R P ∧ Q P ∧ R ( P ∧ Q ) ∨ ( P ∧ R ) T T T T T T T T F T F T T F T F T T T F F F F F F T T F F F F T F F F F F F T F F F F F F F F F 1 P Q R Q ∧ R P ∨ ( Q ∧ R ) T T T T T T T F F T T F T F T T F F F T F T T T T F T F F F F F T F F F F F F F P Q R P ∨ Q P ∨ R ( P ∨ Q ) ∧ ( P ∨ R ) T T T T T T T T F T T T T F T T T T T F F T T T F T T T T T F T F T F F F F T F T F F F F F F F (c) From lecture, ( P unless Q ) ≡ ( ¬ Q ⇒ P ) . P Q ¬ Q ⇒ P P or Q T T T T T F T T F T T T F F F F (d) From lecture, ( P unless Q ) ≡ ( ¬ Q ⇒ P ) . P Q ¬ Q ⇒ P P or Q T T T T T F T T F T T T F F F F HW 2.2 (a) P must be false. Consider the truth table: 2 P Q P ⇒ Q P ⇒ ¬ Q T T T F T F F T F T T T F F T T Consequently, for the two implications to be true at the same time, P must be false. (b) We cannot conclude that S is linear. The phrase “System S is not linear, unless it is ZIZO“ is codified by the implication: ¬ S ZIZO ⇒ ¬ S L which does not say anything about what happens when S ZIZO is true....
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This note was uploaded on 04/02/2008 for the course EECS 20n taught by Professor Babakayazifar during the Spring '08 term at University of California, Berkeley.

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Ee20-hw2-s08-sol - EECS 20N Structure and Interpretation of Signals and Systems Department of Electrical Engineering and Computer Sciences

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