The set X of all binary strings (strings with only 0's and 1's) having the same number of 0's and 1's is defined as follows.
B. λ is in X.
R1. If x is in X, so are 1x0 and 0x1.
R2. If x and y are in X, so is xy.
Give a recursive definition for the set Y of all binary strings with more 0's than 1's. (Hint: Use the set X in your definition of Y.)
B. 0 is in Y.
R1. If y is in Y, so are and yx for any x is in X.
R2. If y1 and y2 are in Y, so is .

Question

The set X of all binary strings (strings with only 0's and 1's) having the same number of 0's and 1's is defined as follows.
B.   	λ is in X.
R1.  	If x is in X, so are 1x0 and 0x1.
R2.  	If x and y are in X, so is xy.
Give a recursive definition for the set Y of all binary strings with more 0's than 1's. (Hint: Use the set X in your definition of Y.)
B.   0  is in Y.
R1.  	If y is in Y, so are   and yx for any x is in X.
R2.  	If y1 and y2 are in Y, so is   .

anonymous · Answer

I don't get R2 for the first one. 
Let x = 1100 in X
     y = 10 in X
but xy = 11000 $\notin $ X
Hence the conclusion R2 is not valid.

perl · Answer

lambda is the empty string

anonymous · Answer

@perl  $\lambda $ is an element in X, we do not know whether it is empty or not. Moreover, if it is in X, it must have 1 and 0 in it.

amilapsn · Answer

R2 means the concatenation of the two strings x & y I suppose.

amilapsn · Answer

R2 about the set Y is incomplete... @XirenitaRockera