Multiple Search Arguments

Hi guys,
I have a logic problem and I cant get my head around it. Maybe one of you clever folks can shed some light on this topic.
Basically I have the following little table that I want people to use to find a pet.
Capture
I would like to have to have a repeating group that display information (on pets) that respond to the user who checks the check boxes. For example someone will like to look for a cat or a dog that is black in color but is also 1-2 years old and 2-3 years old.
The only thing i can think of is having a conditional rule applied to the repeating group that takes into consideration these arguments but the logic to do so is beyond my capabilities. I tried various scenarios but cant figure it out.
Any help will be highly appreciated.
Kind regards,

If checkboxes are a must it can be done, but if you are able to use the free multi-select dropdown things get simpler. Here is a working version of that:

https://toh-samples.bubbleapps.io/version-test/pets?debug_mode=true

It uses a filter, which will work great unless you have a ton of pets in the base search:

The filter is basically checking each pet to see if each of the parameters is contained within the respective choices list OR allowing it in if the parameter is empty. So an OR within the parameter, but an AND across the three parameters.

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Thank you for your time and for the elegant solution provided. Before reading your reply was considering creating a conditional for every single combination but your answer is more than enough for what I have in mind.
Once again, thank you ever so much for your effort and kindness

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