2.2 Set Operations: Discrete Mathematics and its application

modzz
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page.130 Ex.20

Ex.20
Show that if A and B are sets, then (A\capB) \bigcup (A\capB) = A.

how do u solve this?



The Attempt at a Solution

 
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You can't. It's false.
 
modzz:

did you possibly mis-type? Do you mean to show

<br /> (A \cap B) \cup (A - B) = A<br />
 
modzz said:
page.130 Ex.20

Ex.20
Show that if A and B are sets, then (A\capB) \bigcup (A\capB) = A.

how do u solve this?



The Attempt at a Solution


I'm having trouble with this question as well. The second B has a line above it if that means anything. Please help me.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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