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Let $R$ be a ring and let $I \subseteq R$ be a (two-sided) ideal.

Which properties are preserved under taking the quotient $R/I$?

Select ALL that apply.

If $R$ is commutative, then $R/I$ is commutative.

If $R/I$ is commutative, then $R$ is commutative.

If $R$ contains no nontrivial zero divisors, then $R/I$ contains no nontrivial zero divisors.

If $R/I$ contains no nontrivial zero divisors, then $R$ contains no nontrivial zero divisors.

If $R$ is finite, then $R/I$ is finite.