MATH15Aquiz1sol

MATH15Aquiz1sol - valid 1 2(1.4 31 15 points For the...

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Name (Last, First) Please circle your section: A01 A02 A03 A04 5 PM 6 PM 7 PM 8 PM Math 15A Quiz 1 Briggs Fall Quarter 2004 No books, notes, calculators, or any unauthorized assistance is permitted on this quiz. Read each question carefully, answer each question completely, and show all of your work. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If a question is not clear, ask for clarification. GOOD LUCK! 1. (1.3 # 10, 15 points ) Use a truth table to determine whether the following argument form is valid. Indicate which columns represent the premises and which represent the conclusion, and include a few words of explanation to support your work. P R Q R P Q R Solution: In the following truth table, I will use the term “critical row” to describe those in which both premises are both true. premise premise conclusion P Q R P Q P R Q R P Q R T T T T T T T T T F T F F F T F T T T T T T F F T F T F F T T T T T T F T F T T F F F F T F T T T F F F F T T T ←- Critical row. ←- Critical row. ←- Critical row. ←- Critical row. ←- Critical row. In each situation where both premises are true, the conclusion is also true. Therefore, the argument form is
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Unformatted text preview: valid. 1 2. (1.4 # 31, 15 points ) For the circuit corresponding to the Boolean expression ( ∼ P ∧ ∼ Q ) ∨ ( ∼ P ∧ Q ) ∨ ( P ∧ ∼ Q ) there is an equivalent circuit with at most two logic gates. Find such a circuit. Solution: Using the logical equivalences from Theorem 1.1.1, we can reduce the given Boolean expression as follows. ( ∼ P ∧ ∼ Q ) ∨ ( ∼ P ∧ Q ) ∨ ( P ∧ ∼ Q ) ≡ h ∼ P ∧ ( ∼ Q ∨ Q ) i ∨ ( P ∧ ∼ Q ) Distribution Law ≡ ( ∼ P ∧ T ) ∨ ( P ∧ ∼ Q ) Negation Law ≡ ∼ P ∨ ( P ∧ ∼ Q ) Identity Law ≡ ( ∼ P ∨ P ) ∧ ( ∼ P ∨ ∼ Q ) Distribution Law ≡ T ∧ ( ∼ P ∨ ∼ Q ) Negation Law ≡ ∼ P ∨ ∼ Q Identity Law ≡ ∼ ( P ∧ Q ) DeMorgan’s Law The corresponding circuit for the Boolean expression ∼ ( P ∧ Q ) is given by: P Q 2...
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This note was uploaded on 04/14/2008 for the course MATH 15A taught by Professor Briggs during the Fall '04 term at UCSD.

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MATH15Aquiz1sol - valid 1 2(1.4 31 15 points For the...

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