1. ## Discrete (Negation)

Let $P(x,y), R(x,y)$ and $T(x,y)$ be properties which involve reals $x$ and $y$. Negate the following:

$(\forall x)(\exists y)[(P(x,y) \vee T(x,y)) \implies (\sim S(x,y) \wedge R(x,y))]$

Note: you are not allowed to have an implication in answer

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$(\exists x)(\forall y) [(P(x,y) \vee T(x,y)) \wedge (S(x,y) \wedge \sim R(x,y))]$

2. Originally Posted by DiscreteW
Let $P(x,y), R(x,y)$ and $T(x,y)$ be properties which involve reals $x$ and $y$. Negate the following:

$(\forall x)(\exists y)[(P(x,y) \vee T(x,y)) \implies (\sim S(x,y) \wedge R(x,y))]$

Note: you are not allowed to have an implication in answer

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$(\exists x)(\forall y) [(P(x,y) \vee T(x,y)) \wedge (S(x,y) \color{red}\vee \color{black} \sim R(x,y))]$