Easy# Quantifers in Mathematical Proofs

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In mathematical proofs, the word *quantifiers* usually refers to expressions like *for all* and *there exists*. There are standard notations for such expressions, coming from logic.

For example $\forall$ stands for *for all*, $\exists$ stands for *there exists*, $\exists!$ stands for there *exists a unique*, $\nexists$ stands for *there exits no*.

Many mathematicians prefer using the words instead of the symbols when writing proofs, however a knowledge of the formal logical properties of quantifiers can be very useful, or even necessary, when making a rigorous argument.

Let ${\mathbb Z}$ be the set of all integers and ${\mathbb R}$ the set of all real numbers.

Consider the following statements.

Which one is **TRUE**?