Give a recursive definition for the set of all binary strings containing an even
ID: 3793850 • Letter: G
Question
Give a recursive definition for the set of all binary strings containing an even number of 1s.
(Select one or more of the following answers)
If x is a binary string, so is 1x1.
If x is a binary string, so is 0x0, 1x, and x1.
The string 11 belongs to the set
If x is a binary string with an even number of 1s, so is 0x0, 1x, and x1.
If x is a binary string with an even number of 1s, so is 1x1, 0x, and x0.
The string 0 belongs to the set
A.If x is a binary string, so is 1x1.
B.If x is a binary string, so is 0x0, 1x, and x1.
C.The string 11 belongs to the set
D.If x is a binary string with an even number of 1s, so is 0x0, 1x, and x1.
E.If x is a binary string with an even number of 1s, so is 1x1, 0x, and x0.
F.The string 0 belongs to the set
Explanation / Answer
A. True because, if x is binary string it will have even number of ones and appending two more ones will also result in even number of ones in the string.
B. False for 1x and x1. They will result in odd number of ones in the binary string.
C. Yes, it has even numbre of ones
.D. False. Same as B.
E. False and same as above.
F. No ,Zero number of ones is not an even number.
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