Question

in how the other half lives, jacob riis exposed
the different ways people lived in all parts of new york city.
the way that corruption in new york city affected living conditions.
the unsafe conditions in factories in new york city.
the harsh living conditions in new york city slums.

Explanation:

Jacob Riis's How the Other Half Lives focused on documenting the harsh, unsanitary, and overcrowded living conditions in the slums of New York City, especially among the poor immigrant populations. The first option is too broad, the second is about corruption (not the main focus), the third is about factories (which was more of Upton Sinclair's focus), while the fourth accurately reflects what Riis exposed.

Answer:

the harsh living conditions in New York City slums.