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Logical negation question, am I understanding "some not" correctly?

_oshun1__oshun1_ Alum Member
edited February 2018 in Logical Reasoning 3652 karma

I just want to make sure I'm understanding the %s and #s correctly.
Some...not means there exists 0-99% of the two ideas. Some dogs are not friendly means 0-99% of dogs are friendly. 1-100% of dogs are not friendly. there exists at least one dog which is not friendly. Whereas saying all dogs are friendly would mean that 0 dogs are not friendly. 100% of dogs are friendly.

Original statement: Some alphabets are not phonetic.
Lawgic: A <--s--> /P
% meaning: 1-100% of alphabets are not phonetic. 0-99% of alphabets are phonetic.
Number meaning: there exists at least one alphabet which is not phonetic (A & /P)

Negation: A --->P
All alphabets are phonetic.
100% of alphabets are phonetic.
0 alphabets are not phonetic.

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Comments

  • BinghamtonDaveBinghamtonDave Alum Member ⭐ 🍌🍌
    8716 karma

    @"surfy surf" said:

    Original statement: Some alphabets are not phonetic.
    Lawgic: A <--s--> /P
    % meaning: 1-100% of alphabets are not phonetic. 0-99% of alphabets are phonetic.
    Number meaning: there exists at least one alphabet which is not phonetic (A & /P)

    Negation: A --->P
    All alphabets are phonetic.
    100% of alphabets are phonetic.
    0 alphabets are not phonetic.

    This is in my understanding correct. It helps to know these negations both ways: be able to negate the all statement into the "some are not" and also be able to negate the "some are not" into an all statement. A really good example of how important it is to have mastery over this concept is PT 54-2-9.

    David

  • goingfor99thgoingfor99th Free Trial Member
    3072 karma

    All A are B.
    Negation: Some A are not B.

    No A are B.
    Negation: Some A are B.

    Some A are B.
    Negation: No A are B.

    Some A are not B.
    Negation: All A are B.

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