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Define the following point of inequality related to set theory- (a+(1/2)) > 2 ∀...

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rishabh050996 | Student, Grade 10 | eNoter

Posted May 2, 2010 at 11:34 PM via web

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Define the following point of inequality related to set theory-

(a+(1/2)) > 2 ∀ a > 0 and equality holds for a = 1.what does "∀" means?

 

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 2, 2013 at 1:30 PM (Answer #2)

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The logical operator symbol `AA` represents a common quantifier in mathematical logic and it represents that the given proposition is true for any value of variable involved in proposition.

`a + 1/2 >= 2` , `AA a> 0` can be translated as the inequality `a + 1/2 >= 2` holds for any positive value of `a`

You may also notice that the above statement is not valid since not all positive values of `a` make the inequality to hold. Solving the inequality, you may find what are the real positive values of a that make the inequality possible.

`a >= 2 - 1/2 => a >= (4 - 1)/2 => a >= 3/2`

Hence, the given inequality is valid for all `( AA ) a>= 3/2` .

Hence,as a conclusion regarding the logical operators, the logical quantifier `AA` as well as the existential quantifier `EE` represents the most common two logical operator symbols in theory of sets.

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alpavasavada | High School Teacher | eNotes Newbie

Posted November 15, 2010 at 3:06 PM (Answer #1)

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As per the question,

a + o.5 can never be equal to 2 for a = 1. It is 1+0.5 = 1.5.

∀ means for all.

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