Logic: Possible Typo in Textbook

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It's possible that I'm not understanding the diagram and their reasoning, but I wanted to check with some people here before I come to a conclusion.

Homework Statement



Klenk-PF.jpg


Homework Equations


The Attempt at a Solution



I don't understand why the book says the formula is false, yet there is a "T" at the bottom of the computation.

The book is, Understanding Symbolic Logic, 5th ed. by Virginia Klenk.
 
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The 'T' at the bottom of the diagram is a typo. It should be an 'F'. The words you highlighted are correct.
 
Stephen Tashi said:
The 'T' at the bottom of the diagram is a typo. It should be an 'F'. The words you highlighted are correct.

Thank you for verifying, Stephen.
 

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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