Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive 0s and two consecutive 1s?

A string contains two consecutive 0s (00) and two consecutive 1s (11) if either:

1. 00 appears before 11, represented by: $(0 + 1)^*00(0 + 1)^*11(0 + 1)^*$

2. 11 appears before 00, represented by: $(0 + 1)^*11(0 + 1)^*00(0 + 1)^*$

Taking the union of these two forms and factoring out the common prefix $(0 + 1)^*$ and suffix $(0 + 1)^*$, we get:

• Option (A) requires 00 and 11 to be immediately adjacent (0011 or 1100), which fails to match valid strings like 001011.

• Option (C) represents strings containing 00 OR 11, not both.

• Option (D) requires strings to start with 00 or 11 and end with 11 or 00, missing strings like 100110.

Thus, (B) is the correct option.