Many people assume that individuals with Aspergers cannot empathize.  This is not true. 

Just like their typical peers, they can empathize and sympathize by relating their emotions with their experiences.  The difference lies not in their ability to relate emotionally but in their ability to grasp the perspective of others. 

If they, themselves, have experienced a similar emotional experience, they can "relate" and react with shared emotion.  If they have not had a similar experience, they might lack the ability to perceive another's state of mind and therefore, not react appropriately.

For example, if a child with Aspergers has never had a pet, they might not understand the sadness another might feel over the death of their pet.  If they have a pet; however, they would likely "understand" another's loss and empathize.