$$\exists x\in\chrischona2015.orgbbR \; \forall y\in\chrischona2015.orgbbR, \; x^2+y^2\leq 1 \Rightarrow xy\neq 0$$
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?)
edited Sep 20 in ~ 20:01
inquiry Sep 20 at 19:43
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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.
answer Sep 20 at 20:22
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