Let s be a nonempty subset of real number set R. if x, y belong to s, x + y, X-Y, XY belong to s, then s is called a closed set 1. The set s = {the root of a + B is 3 | a, B is an integer} is a closed set; 2. If s is a closed set, then 0 must belong to s; 3. A closed set must be an infinite set; 4. If s is a closed set, then any set t satisfying s contained in T and R is also a closed set The true proposition is------

Let s be a nonempty subset of real number set R. if x, y belong to s, x + y, X-Y, XY belong to s, then s is called a closed set 1. The set s = {the root of a + B is 3 | a, B is an integer} is a closed set; 2. If s is a closed set, then 0 must belong to s; 3. A closed set must be an infinite set; 4. If s is a closed set, then any set t satisfying s contained in T and R is also a closed set The true proposition is------

1. Correct proof: let x, y ∈ s, let x = a + B √ 3, y = C + D √ 3, then x + y = (a + C) + (B + D) √ 3, since a, B, C, D are all integers, then a + C, D + B are also integers, so x + y ∈ SX + y = (A-C) + (B-D) √ 3, since a, B, C, D are all integers, then a-c, D-B are also integers, so X-Y ∈ sxy = AC + 3bd + (AD + BC) √ 3