What is the inverse of this statement:
The case $Q$ is true if and only if there exist $θ∈ℝ$ such that the property $P=P(θ)$ is verified.
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I'm not sure if "converse" is the term you want. Do you want to know how to negate both sides? – BrianO Oct 05 '15 at 15:31
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@BrianO: Yes, I wante to negate both sides. – DER Oct 05 '15 at 15:31
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http://math.stackexchange.com/questions/10435/negation-of-if-and-only-if – R.N Oct 05 '15 at 15:35
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Neither "converse" nor "inverse" quite work when applied to biconditionals. To negate both sides:
$$\neg Q \iff \forall \theta \in \mathbb R: \neg P(\theta) $$
In other words, $Q$ is false iff for all reals $\theta$, $P(\theta)$ does not hold.
BrianO
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