Final answer:
The Portuguese were the first Europeans to explore beyond Europe's borders, making the initial claim true. However, the majority of natives killed during the exploration period were due to diseases, not directly by European weapons, making the other claim false. Pedro Cabral was the explorer who claimed Brazil for Portugal.
Step-by-step explanation:
The statement that the Portuguese became the first Europeans to explore beyond Europe's borders is true. Under the sponsorship of Prince Henry the Navigator, the Portuguese utilized advances in navigational technology such as the compass, the astrolabe, and the caravel to explore the coast of Africa in the early 1400s. This set into motion the European Age of Discovery, where the Portuguese first established trading posts along the coast of West Africa and later in India. After their exploratory successes in Africa, Pedro Cabral unintentionally reached the shores of Brazil in 1500, which he claimed for Portugal. This era of exploration led to Portugal and Spain dividing the world into zones of influence through the Treaty of Tordesillas and later the Treaty of Zaragosa.
Regarding the exploration period and the interaction with native populations, while the Europeans did have superior weapons, it was the spread of diseases brought by the Europeans that killed the majority of the native populations, making the assertion that the majority were slaughtered by European weapons false.
The first explorer to reach Brazil and claim it for the throne of Portugal was Pedro Cabral, not Christopher Columbus, Ferdinand Magellan, or Jacques Cartier.