How do I send different information in the same email based on tags?

I want to be able to send an email to all my contacts within a specific tag. But I also want to add certain information if they are also tagged with something else.

For example,
I want to send everyone that I have tagged as “Dog lovers” an email. If these contacts are also tagged with “Dog owner”, I want to add a coupon for free dog food to the bottom of the same email.

Is this possible or do I need to send two separate emails?