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# Negate and Simplify?

Negate the following and simplify

p∨q∨(¬p∧¬q∧r)

### 2 Answers

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- cmcsafeLv 71 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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