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Two questions

(1)For R a ring and A a subset of R, let s(A) denote the set of all subrings of R that contain A (including R itself). Show that the intersection of all these subrings is itself a subring of R.

(2)Suppose that 1 is not equal to 0 in R. Show that the sets ∅, {0} and {1} all generate the same ring in R.

(1)For R a ring and A a subset of R, let s(A) denote the set of all subrings of R that contain A (including R itself). Show that the intersection of all these subrings is itself a subring of R.

(2)Suppose that 1 is not equal to 0 in R. Show that the sets ∅, {0} and {1} all generate the same ring in R.

Thanks