Question 1. (a) Prove that if r E R satisfies x" + a,-1ª"-1 +...+ ao = 0 for some integers a„-1, … . , ao and r 4 Z, then x must be an irrational.

Q: Determine the positive real numbers x and y such that • x + y = 4 and 2.n2 + y² is small as…

A:

Q: 8. A (5+, 10-) where A-Z 9. Ax [5+, 10-] where A = Z' 10. Ax=(1, 10) where A = (0,1)

A: These are the problems from the Set Theory.

Q: Prove that 2n+l > (n + 2) · sin(n) for all positive integers n.

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