Need answers for these easy questions.

Need answers for these easy questions.

Q1: Fill in the blank.

Give a recursive definition for the set X of all natural numbers that are one or two more than a multiple of 10. In other words, give a recursive definition for the set {1, 2, 11, 12, 21, 22, 31, 32, … }.

B1.  1 is in X.

B2. _________ is in X.

Q2: 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.

List all elements of 
X. (Enter your answers as a comma-separated list.) 

Q3: Define a set X recursively as follows.

B.  12 
 X.

R1. If x 
 X and x is even, then x/2 
 X.

R2. If x 
 X and x is odd, then x+1 
 X.

List all elements of 
X. (Enter your answers as a comma-separated list.)

Q4: Use a decision tree to count the number of strings of length 3 using the symbols a, t, and e with the restriction that et, at, and ta do not appear anywhere in the string.

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