I've attached the file. I only need help with f), g), h), i), j), k)
Yfrog - problemrw
Let me know if this link works.
It does!
I'll help you with f, g. Try the rest and get back to us.
f) is the set of all real numbers $\displaystyle x$ such that $\displaystyle x^2\not <2$ and $\displaystyle x^2\not >2$. Think about it, this is saying that $\displaystyle x^2\leqslant 2$ and $\displaystyle x^2\geqslant 2$ and so $\displaystyle x^2=2\implies x=\pm\sqrt{2}$
g) Notice that $\displaystyle E$ and $\displaystyle D$ are disjoint and so every thing that is in $\displaystyle E$ that isn't in $\displaystyle D$ is just $\displaystyle E$. And so, $\displaystyle \mathbb{R}-\left(E-D\right)=\mathbb{R}-E$ and so it's all the numbers for which $\displaystyle x^2\not >2\implies x\in [-\sqrt{2},\sqrt{2}]$
f) Read it as "The reals, excluding those in E, excluding those in D".
g) Read it as "The reals, excluding (those in E, excluding those in D)". What do you think the brackets mean?
h) Read it as "The rationals, excluding those in the Reals" (what do you think THAT would leave?) or those in C.
i) Read it as "Everything that is in C and not in A".
j) Read it as "Everything in E and not in D"
k) Read it as "Everything in A or not in B".
Hi Prove it,
The answer is just C, right?
I'm having some problems with the remaining questions - so for i), it's what's in C and not what's in A, so how do I get the answer to this? So 0 and 1 in C are gone, so how do I write the answer? It's the inequalities that are messing me up.