# Really Real Numbers!

Algebra Level 4

$$a$$ and $$b$$ are two real numbers. Read the following statements about them.

$$[1].$$ If $$a>b$$ and none of them are equal to zero, then $$\dfrac{1}{a}<\dfrac{1}{b}$$.

$$[2]$$. The equation $$\sin^{-1} (a)+\cos^{-1} (a)=\dfrac{\pi}{2}$$ holds for all real numbers $$a$$.

$$[3]$$. $$\dfrac{a}{b}$$ is always a real number.

Which of these statements are true?

Details and assumptions:

The statements are independent. That means if according to statement $$[1]$$, $$a=2$$; it applies to statement $$[1]$$ only.

This problem is from the set "MCQ Is Not As Easy As 1-2-3". You can see the rest of the problems here.

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