Universal and Existential quantifier in Propositional logic **The following paragraph is an excerpt from Discrete Mathematics book of Kenneth Rosen 7edition** > The restriction of a universal quantification is the same as the universal quantification of a conditional statement. For instance, ∀x < 0 (x2 > 0) is another way of expressing ∀x(x < 0 → x2> 0). On the other hand, the restriction of an existential quantification is the same as the existential quantification of a conjunction. For instance, ∃z > 0 (z2 = 2) is another way of expressing ∃z(z > 0 ∧ z2 = 2). **Ques : Why universal quantification is same as universal quantification of a conditional statement whereas existential quantification is same as existential quantification of a conjunction?** Please provide proper details. Thank You.

Think on these lines.

$(1)$ All humans die.

Equivalent form : For every $x$, _if_ $x$ is human, _then_ $x$ must die. **(An implication)**

$(2)$. Some animals are color blind.

Equivalent form: There exists some $x$ such that, $x$ is an animal _and_ $x$ is color blind. **(A conjunction)**