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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