Give a recursive definition of the set of positive integers that are multiples of 4.

4∈S, and x+y∈S if x,y∈S.
4∈S, and x+8∈S if x∈S.
4∈S, and xy∈S if x,y∈S.
4∈S, and 4x+4∈S if x∈S.
4∈S, and 4x∈S if x∈S.

Question

Give a recursive definition of the set of positive integers that are multiples of 4.
 
 
		4∈S, and x+y∈S if x,y∈S.
		4∈S, and x+8∈S if x∈S.
		4∈S, and xy∈S if x,y∈S.
		4∈S, and 4x+4∈S if x∈S.
		4∈S, and 4x∈S if x∈S.

vortish · Answer

@jim_thompson5910  do you have any knowledge on how to do these\