Mathematical Awareness #2

Statement \(\color{red}{S:}\) All real transcendental numbers are irrational numbers.

Statement \(\color{red}{A:}\) Some irrational numbers are transcendental numbers.

Statement \(\color{red}{N:}\) \((\sqrt{-1})^{\sqrt{-1}}\) is not a transcendental number.

Statement \(\color{red}{D:}\) \((\pi+e)\) and \((\pi \times e)\) : Both are not transcendental numbers.

Statement \(\color{red}{E:}\) \(\sqrt{2}\) and \(\sqrt{3}\) are both transcendental as well as irrational numbers.

Statement \(\color{red}{E:}\) Sum of two transcendental numbers is always a transcendental numbers.

Statement \(\color{red}{P:}\) Some irrational numbers are not transcendental numbers.

Which of the above statements are correct?

Note : There are two statements above named as "E". It is provided that either both the "E" statements are correct or both are incorrect. In the former case "EE" will be included in the answer and in the later case, no "E" statement will be counted in the answer.

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