Given set A is P a partition of A

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For the given set A, determine whether P is a partition of A.

A= {1,2,3,4}, P={{1,2},{2,3},{3,4}}

Is it correct to say that P is a partition of A?

Thank you
 
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What is the definition of a partition? It should make the answer apparent.
 
Last edited:
Let A be a nonempty set. P is a partition of A iff P is a set of subsets of A such that

i. if X \inP, then X ≠∅
ii. if X \inP and if Y \inP, then X=Y or X\capY=∅
iii. X\inP\bigcupX=A
 
Are there any two elements X,Y of P such that X∩Y≠∅ ?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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