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Bashyboy
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Homework Statement
Express each of these mathematical statements using predicates, quantifiers, logical connectives, and mathematical operators.
c) Every positive real number has exactly two square roots.
d) A negative real number does not have a square root that is a real number.
Homework Equations
The Attempt at a Solution
For part c), the answer in the textbook is, [itex]\forall x \exists a \exists b(a ≠ b \wedge \exists c(c² = x ↔ (c = a \vee c = b)))[/itex] my answer is, [itex]\forall x \exists y \exists z [((x > 0) \wedge (a \ne b)) \implies ((\sqrt{x} = y) \wedge (\sqrt{x} = z))][/itex]
For part d), the answer in the textbook is, [itex]\forall x ((x < 0) \implies \neg \exists y (x = y^2))[/itex]; my answer is, [itex]\forall x[(x < 0) \implies (\sqrt{x} \notin \mathbb{R})[/itex]
I was wondering, are my answers as valid as the ones provided in the textbook?
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