"Nothing can be loved or hated unless it's first understood."– Leonardo Da Vinci

awashing November 15, 2016

L or H negation?

I thought the rule was that when unless was introduced loved or hated should have been negated as the sufficient condition but in the answer response it appears to have stayed the same. Is that because there was also a "No" in front of the sufficient condition so the double negative made it just L or H? Could someone clarify?

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Mehran November 15, 2016

@awashing what follows "unless" is our necessary condition and you are correct that we must negate the other part of the statement to create the sufficient condition.

The other part of the statement here is, "Nothing can be loved or hated . . . "

The correct negation of this would be, "Something can be loved or hated."

Remember, the logical opposite of "nothing" is "something."

Hope that helps! Please let us know if you have any other questions.

awashing November 18, 2016

Makes sense - thank you!

kadeemmaliek April 12, 2017

That makes sense- but in negativity, don't we change the or to &? It appears to be wrong; clarity would really help

Mehran April 21, 2017

Generally, that is correct. When you negate "and" it becomes "or" and vice versa.

Here, however, you are not negating just "L or H."

Rather, you are negating "nothing L or H."

The logical opposite of of "nothing" is "something" so the negation would be "something L or H" (i.e. L or H).

Hope that helps! Please let us know if you have any other questions.

Mazen March 3, 2020

Is there a lesson that addresses logical opposites of words such as "nothing, something, everything." Specific terminology such as the ones quoted above are not addressed in the lessons on "sufficient and necessary, or, quantifiers." Which lesson would they be under?

ohanamgt July 28, 2021

Yes I believe you have analyzed this correctly. The no, creates a positive term after the negation. Tricky!

ohanamgt July 28, 2021

Yes you have analyzed this correctly. The no, creates now a positive term in the sufficient after the negation. Tricky!