Part CCSIR NET December 2024euclidean-stops-at-one-variable

Euclidean stops at one variable

Which of the following statements are true?

A.The value of the Euler $φ -$ function is even for all integers n ≥ 3.✓
B.Let G be a finite group and S a subset of G with |S| > |G|/2. Then {ab : a, b ∈ S} = G.✓
C.The polynomial ring $R [x_{1}, \dots, x_{n}]$ is a Euclidean domain for all integers n ≥ 1.
D.The subset {f ∈ C([0, 1]) : f(1/2) = 0} of the ring C([0, 1]) of continuous functions from [0, 1] to $R$ is a prime ideal.✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

50 are analysed free — try those first.

More on this topic