$$\exists x\in\chrischona2015.orgbbR \; \forall y\in\chrischona2015.orgbbR, \; x^2+y^2\leq 1 \Rightarrow xy\neq 0$$

The negative of that (i.e.)$$\lnot(\exists x\in\chrischona2015.orgbbR \forall y\in\chrischona2015.orgbbR, \; x^2+y^2\leq 1 \Rightarrow xy\neq 0)$$

should it is in (not sure if this is correct)$$\forall x\in\chrischona2015.orgbbR \; \exists y\in\chrischona2015.orgbbR, \; x^2+y^2\leq 1 \land xy=0$$

Which of this statements is true? I"m having actually trouble figuring that out.

You are watching: Which of these statements is true?

The very first one should be false because if $x=0$ and $y climate $x^2+y^2$ will be true however $xy$ will certainly still same $0$ and be false.

In the 2nd one if $x>1$ and also $y=0$ climate $x^2+y^2$ will be higher than$1$ (be false) and $xy$ will equal $0$ (true), therefore all together it"s false (for connect to be true both need to be true, right?)


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For $\forall x\in\chrischona2015.orgbbR \; \exists y\in\chrischona2015.orgbbR, \; x^2+y^2\leq 1 \land xy=0$, take into consideration $x = 2$. As $\forall y \in \chrischona2015.orgbbR, 4 + y^2 \gt 1$, this statement is false. Thus its negation (the an initial statement) is true.


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