(1) Let p= prime integer. Let T= the set of rational numbers (in lowest terms) w

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(1) Let p= prime integer.

Let T= the set of rational numbers (in lowest terms) whose denominators are not divisible by p.

Let I= the set of elements of T whose numerators are divisible by p.

(1) Let p= prime integer. Let T= the set of rational numbers (in lowest terms) whose denominators are not divisible by p. Let I= the set of elements of T whose numerators are divisible by p. Prove T/I cong mathbb{Z}p (2) Let I= set of matrices of the form bigl(begin{smallmatrix} 0&b; 0&0 end{smallmatrix}bigr) with b in mathbb{R} Let S= set of matrices of the form bigl(begin{smallmatrix} a&b; 0&c; end{smallmatrix}bigr) with a, b, c in mathbb{R} Prove S/I cong mathbb{R} X mathbb{R}

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