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    MMW Assessment

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    Kathleen Capulong
    The document contains 4 problems regarding propositional logic and truth tables. Problem 1 has students write out logical statements in words and draw implications between statements. Problem 2 has students construct truth tables for logical statements. Problem 3 uses a truth table to show the logical equivalence of two expressions. Problem 4 uses truth tables to prove De Morgan's laws.

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    MMW Assessment

    Uploaded by

    Kathleen Capulong
    340 views3 pages
    The document contains 4 problems regarding propositional logic and truth tables. Problem 1 has students write out logical statements in words and draw implications between statements. Problem 2 has students construct truth tables for logical statements. Problem 3 uses a truth table to show the logical equivalence of two expressions. Problem 4 uses truth tables to prove De Morgan's laws.

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    Proposition Assesment

    Original Title

    MMW ASSESSMENT

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    The document contains 4 problems regarding propositional logic and truth tables. Problem 1 has students write out logical statements in words and draw implications between statements. Problem 2 has students construct truth tables for logical statements. Problem 3 uses a truth table to show the logical equivalence of two expressions. Problem 4 uses truth tables to prove De Morgan's laws.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    340 views3 pages

    MMW Assessment

    Uploaded by

    Kathleen Capulong
    The document contains 4 problems regarding propositional logic and truth tables. Problem 1 has students write out logical statements in words and draw implications between statements. Problem 2 has students construct truth tables for logical statements. Problem 3 uses a truth table to show the logical equivalence of two expressions. Problem 4 uses truth tables to prove De Morgan's laws.

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    © All Rights Reserved
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    ASSESMENT 2

    1. Write each statement in words. Let p: The plane is on time. Let q: The sky is clear.

    a) p ∧ (¬q)
    - The plane is on time and the sky is not clear.

    b) q → (p ∨¬p)
    - The sky is clear, then the plane is on time or the plane is not on time.

    c) p ↔ q
    - The plane is on time if and only if the sky is clear.

    d) p → q
    - The plane is on time, ten the sky is clear.

    2. Construct a truth table for each proposition.

    a) p → ¬ q
    p q ¬q p→¬q
    1 1 0 0
    1 0 1 1
    0 1 0 0
    0 0 1 1

    b) [(p ∧ ¬q) → r
    p q r ¬q p ∧ ¬q (p ∧ ¬q) → r
    1 1 1 0 0 1
    1 1 0 0 0 0
    1 0 1 1 1 1
    1 0 0 1 1 0
    0 1 1 0 0 1
    0 1 0 0 0 0
    0 0 1 1 0 1
    0 0 0 1 0 0
    c) (p ∧ q) ∨ r]↔[(p ∧ r) ∨ (q ∧ r)]
    p q r p ∧q p∧r q ∧ r (p ∧ q) ∨ r (p ∧ r) ∨ (q ∧ r) (p ∧ q) ∨ r]↔[(p ∧ r) ∨ (q ∧ r)
    1 1 1 1 1 1 1 1 1
    1 1 0 1 0 0 1 0 0
    1 0 1 0 1 0 1 1 1
    1 0 0 0 0 0 0 0 1
    0 1 1 0 0 1 1 1 1
    0 1 0 0 0 0 0 0 1
    0 0 1 0 0 0 1 0 0
    0 0 0 0 0 0 0 0 1

    d) [(p ∧ r ) → (q ∧ ¬r )] → [(p ∧ q) ∨ r )]
    p q r ¬r p∧ r q ∧ ¬r p∧ q (p ∧ q) ∨ r (p ∧ r ) → (q ∧ ¬r ) (q ∧ ¬r )] → [(p ∧ q) ∨ r )
    1 1 1 0 1 0 1 1 0 1
    1 1 0 1 0 1 1 1 1 1
    1 0 1 0 1 0 0 1 0 1
    1 0 0 1 0 0 0 0 0 0
    0 1 1 0 0 0 0 1 0 1
    0 1 0 1 0 1 0 0 1 0
    0 0 1 0 0 0 0 1 0 1
    0 0 0 1 0 0 0 0 0 0

    3. Using the truth table prove that the following propositions are logically
    equivalent: p ∨ (q ∧r)⇐ ⇒ (p ∨q) ∧ (p ∨r)

    p q r q ∧r p ∨q p ∨ (q ∧r) (p ∨q) ∧ (p ∨r)


    1 1 1 1 1 1 1
    1 1 0 0 1 1 1
    1 0 1 0 1 1 1
    1 0 0 0 1 1 1
    0 1 1 1 1 1 1
    0 1 0 0 0 0 0
    0 0 1 0 1 0 0
    0 0 0 0 0 0 0
    4.Prove the De Morgan’s Laws by constructing truth tables.
    ¬ (p∧q) = ¬p∨ ¬q
    ¬ (p∨q) = ¬p∧ ¬q

    p q ¬p ¬q p∧q ¬ (p∧q) ¬p∨ ¬q


    1 1 0 0 1 0 0
    1 0 0 1 0 1 1
    0 1 1 0 0 1 1
    0 0 1 1 0 1 1

    p q ¬p ¬q p∨q ¬ (p∨q) ¬p∧ ¬q


    1 1 0 0 1 0 0
    1 0 0 1 1 0 0
    0 1 1 0 1 0 0
    0 0 1 1 0 1 1

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