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?
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.