Define a set X of integers recursively as follows B 10 is in

Define a set X of integers recursively as follows.

B. 10 is in X.

R1. If x is in X and x > 0, then x 3 is in X.

R2. If x is in X and x < 0, then x + 4 is in X.

So, X will be of that type of Set, in which all type of negative and positive values will be there..

Lets take x=1, this means x>0, then 1-3=-2 will be in X

x=2, this means 2-3=-1 will be in X

x=3, this means 3-3=0 will be in X

x=4, this means 4-3=1 will be in X

and lets take x=-1, this means x<0, then -1+4=3 will be in X

x=-2, this means -2+4=2 will be in X

x=-3 this means -3+4=1 will be in X

x=-4 this means -4+4=0 will be in X

x=-5 this means -5+4=-1 will be in X

So, for R2, X = {.........,-1,0,1,2,3}

for R1,X={-2,-1,0,1,2,3,4,5,6,7,8,9,10,11,....... }