Living organisms share several characteristics, but not all of the options listed are universally shared by all living organisms. Let's break it down:
Hereditary information is passed to offspring: This is a shared characteristic among living organisms. Reproduction and passing on genetic information to offspring is a fundamental aspect of life.
Adaptation to environmental change: While many living organisms have the ability to adapt to their environment, it's not a universal characteristic. Some organisms may not have the ability to adapt to changes in their environment.
Requirement for nutrients: All living organisms require nutrients for survival, so this is a shared characteristic.
DNA housed in a nucleus: This is not a universal characteristic. Organisms are classified into two main categories: prokaryotes and eukaryotes. Prokaryotes do not have a nucleus, while eukaryotes do. Therefore, the presence of a nucleus is not shared by all living organisms.
Based on the shared characteristics among all living organisms, the correct options are:
I and III
So, hereditary information passed to offspring and adaptation to environmental change are characteristics shared by all living organisms.