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If a statement was all triangles have three sides and three angles, then the negation of p (p) would be all triangles do not have three sides and three angles.

a. true
b false

User MarZab
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1 Answer

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Final answer:

The negation of "All triangles have three sides and three angles" is false; the correct negation is "There exists at least one triangle that does not have three sides and three angles".

Step-by-step explanation:

The negation of the statement "All triangles have three sides and three angles" would not be "All triangles do not have three sides and three angles". Instead, the correct negation would be "There exists at least one triangle that does not have three sides and three angles", which properly negates the universality of the original statement by referencing the existence of even a single counterexample.

The original question suggests a common misconception about negation in logic. Simply putting "not" in front of the whole statement does not work when we are dealing with universal qualifiers such as "all". Negation generally involves suggesting the existence of an exception to the original universal claim.

User Galex
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