Which characteristic do all prokaryotes and eukaryotes share?
the need to acquire energy from other organisms

the need to take in oxygen for cellular respiration

the ability to transmit genetic information to an offspring

the ability to reproduce through sexual reproduction

The correct options are the need to take in oxygen for cellular respiration and the ability to transmit genetic information to an offspring.

Explanation:

Both prokaryotes and eukaryotes use oxygen to carry out aerobic respiration.The major byproduct of aerobic respiration in case of both prokaryotes and eukaryotes is Carbon dioxide(CO2).

Both prokaryotes and eukaryotes have the ability to transmit information to their off springs.Most  Eukaryotes carry out the same by sexual reproduction and prokaryotes exhibit the same by binary fission.