[Math] How to find the distinct equivalence classes for the set of all bit strings of length 5

Question

Let B denote the set of all bit strings of length 5,
$b_1,b_2,b_3,b_4,b_5$. Define a relation R on B by: two bit strings
are related by R if and only if they both have bits $b_1$ the same and both have
the bits $b_5$ the same.

(a) List all the elements of the equivalence class [10010].

(b) How many distinct equivalence classes are there? List them.

So we never went over bit strings in class and I'm trying to apply the same concepts as a similar question that had integers and ordered pairs.

For part (a), the elements of the equivalence class [10010] is just 0 and 1?

For part (b), the distinct equivalence classes are all of the variations of the 5 bit strings where bits $b_1$ and $b_5$ are the same? for example, [10010] and [11110]? How would I go about determining the exact number of distinct equivalent classes?

Any help is appreciated,

thanks in advance

Answer 1

SOLUTION:

(a) [10010] [10110] [10100] [10000] [11000] [11100] [11010] [11110]

(b) 4 distinct equivalence classes. [10000] [10001] [00000] [00001]