Math

QuestionRewrite the statement and provide its negation: All people are temperamental.

Studdy Solution

STEP 1

Assumptions1. The given statement is "All people are temperamental." . We need to express this statement in an equivalent way.
3. We also need to write the negation of this statement.

STEP 2

First, let's express the given statement in an equivalent way. The statement "All people are temperamental" can be equivalently expressed as "There does not exist a person who is not temperamental."
x,(x)\forall x,(x)Where- \forall denotes "for all" - xx denotes "people" - (x)(x) denotes "is temperamental"
This can be equivalently expressed as¬x,¬(x)\neg \exists x, \neg(x)Where- ¬\neg denotes "not" - \exists denotes "there exists"

STEP 3

Now, let's write the negation of the original statement. The negation of "All people are temperamental" is "There exists a person who is not temperamental."
¬(x,(x))\neg (\forall x,(x))This can be equivalently expressed asx,¬(x)\exists x, \neg(x)So, the equivalent statement is "There does not exist a person who is not temperamental" and the negation is "There exists a person who is not temperamental."

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