Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 year ago

Negate and Simplify?

Negate the following and simplify

p∨q∨(¬p∧¬q∧r)

2 Answers

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  • MyRank
    Lv 6
    1 year ago

    Given,

    Attachment image
  • 1 year ago

    Negate

    ¬(p∨q∨(¬p∧¬q∧r))=

    As¬(p∨q)=¬p∧¬q

    =¬p∧¬q∧¬(¬p∧¬q∧r)=

    Simplify

    =¬p∧¬q∧(p∨q∨¬r)=

    As a∧(b∨c)=(a∧b)∨(a∧c)

    =(¬p∧¬q)∧(p∨q)∨(¬p∧¬q∧¬r)=

    As (¬p∧¬q)∧(p∨q)=False

    =(¬p∧¬q∧¬r)=

    =¬(p∨q∨r)

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