Which layer is known as the strong lower part of the mantle?

The strong lower part of the mantle is referred to as the mesosphere. This region lies beneath the upper mantle and extends down to the outer core. The mesosphere is characterized by its solid state, which can withstand significant pressure, making it stronger than the upper mantle layers above it.

In contrast, the other layers mentioned in the options do not pertain to the Earth's mantle. The troposphere is the lowest part of the Earth's atmosphere, where weather occurs. The stratosphere, lying above the troposphere, contains the ozone layer and has a different composition and behavior than the mantle. The ionosphere, meanwhile, is a region of the atmosphere ionized by solar radiation, which also does not relate to the Earth's mantle in terms of physical properties or location. Thus, referring to the mesosphere as the strong lower part of the mantle is accurate, as it accurately reflects the characteristics and location of this part of the Earth's structure.