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Lv 4
? asked in Science & MathematicsMathematics · 8 years ago

Check if the following statements are tautology or contradiction.?

a) (~p ˅ q) ˅ (p ˄ ~q)

b) (p ˄ q) → (p ˅ q)

I'd really appreciate it if you could show me the working.

1 Answer

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  • Peter
    Lv 4
    8 years ago
    Favorite Answer

    You can do these by using truth tables or Boolean algebra. As there are only 2 variables and so only 4 cases I will use truth tables.

    a)

    p q (~p ˅ q) (p ˄ ~q) (~p ˅ q) ˅ (p ˄ ~q)

    T T T F T

    T F F T T

    F T T F T

    F F T F T

    Always true, tautology

    p q (p ˄ q) (p ˅ q) (p ˄ q) → (p ˅ q)

    T T T T T

    T F F T T

    F T F T T

    F F F F T

    Also a tautology.

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