According to the question, Yuriko Koike is identified as the individual who recently took charge as the first Woman Prime Minister of Japan.
Yuriko Koike is a prominent Japanese political leader known for her long-standing role in public administration and governance. She has previously held key ministerial positions and has been widely recognized for her leadership abilities, administrative experience, and reform-oriented approach.
Her appointment is considered a historic milestone, as it represents a significant step forward for women’s political representation in Japan, a country where top executive leadership roles have traditionally been dominated by men.
The other options listed—Sanae Takaichi, Renho Murata, and Seiko Noda—are also influential political figures in Japan, but they have not been identified in this context as having assumed the office of Prime Minister.
Therefore, the correct answer is:
\(\boxed{(a)\ \text{Yuriko Koike}}\)