CF1344C Quantifier Question

Logical quantifiers are very useful tools for expressing claims about a set. For this problem, let's focus on the set of real numbers specifically. The set of real numbers includes zero and negatives. There are two kinds of quantifiers: universal ( $ \forall $ ) and existential ( $ \exists $ ). You can read more about them here. The universal quantifier is used to make a claim that a statement holds for all real numbers. For example: - $ \forall x,xx-1 $ is read as: for all real numbers $ x $ , $ x $ is greater than $ x-1 $ . This statement is true. The existential quantifier is used to make a claim that there exists some real number for which the statement holds. For example: - $ \exists x,xx-1 $ is read as: there exists a real number $ x $ such that $ x $ is greater than $ x-1 $ . This statement is true. Moreover, these quantifiers can be nested. For example: - $ \forall x,\exists y,x

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For the first test, the statement $ \forall x_1, \exists x_2, x_1