Determining a given subset is partition or not?

Question

Which of these collections of subsets are partitions of the set of bit strings of length 8?

(a) the set of bit strings that end with 00, the set of bit strings that end with 01, the set of bit strings that end with 10, and the set of bit strings that end with 11.

(b) the set of bit strings that end with 111, the set of bit strings that end with 011, and the set of bit strings that end with 00

Answer: a is a partition

Confusion is, why b is not a partition. We know that, the elements of different partition must be unique and union of all partition should be equal to the set itself. I can't find any overlapping elements between different partition of (b) and if there is any, then why not in (a).

Answer 1

Disjoint Union of suset is called Partition.

 In option (a)  they are saying set of bit string end with 00, 01, 10, 11 .Option (a) is definitely partition of 8 bit string. Becouse they are disjoint as well as union of all subsets givesAll bit string of length 8.

In option (b) they are saying set of bit string ends with 111, 011 , 00 . Yes these are disjoint but combination of all (i.e. Union) is not same as Statement (all 8 bit string). So it is not partition.