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# [Jelly], 10 bytes

    ṭŒcg/€ċ1=1

[Try it online!][TIO-lplssr7r]

[Jelly]: https://github.com/DennisMitchell/jelly
[TIO-lplssr7r]: https://tio.run/##bVW7blNBEO3zFVepQezs7t1HIij5AoREiVCEhFwRUdAFmhR0oYUGWmgQBRESTTD/Yf@ImTN7r@/M2lJsySdnZ86cmZ19dbFavd3tNrff1zcvXj7Yvv/29wM9pN364@b26/bdn@Fs8@vL@ubp3fXJ5vfP8@3Vp@H@o2F79fn87vrfD6Y/2@3o3oC/4Ww4ffx8dXlxetIQf4AEi/gDjrccf8DxxzjhGBIPkNEi8RiStB6fWfX0pfHC4TheKQCfvH4DzDHoHVPduKAVzB70UJMQYsGKn4hegZGBceSwXmEjSIi4YIGzjKwyKz2BeYXrKYqH39Ct47EyPtwRPaurUFgVEfUxRpQXcGSFmQNElbny78zE7CwPAaOyoTAvcOLYKSQXbWaUnFGyrhlAQt2kZDenWaeSA3nkxDF1vM5Uip0XnAXOqQAFtXBQ6pgoyBwnaaCznc2uNYJGa0fqpqKlsBbFI6lhLUnDVWY0JvMEpLSACQPKKpWTaH6WcVY8kOCmFo0JS7gxmufa2BrVYXYsKzkog1CyagN6hY7rqWitKXb2ZM44QC12HkM3j7gttVhv4CthrJJt34jVozoVYzurRZMoRl@NGpEIg1QWPkxzddNKQIa4Vz2BCV2RtaDAff@c2TRzcgPjXiKoXm7JtUx8TfpVlfx8m2a0bQqwvV6iue2QHLulJlfX7HGPiYl2vaLWXPmjMP6Zcld@yDLlVSuKQSqKevHKUGERxO4wdJOWg2VYKvaQTo0tGeZLP4EltBKDqaYioLdrv8KiOt@TOREaBLaPtkhyuFb6vAywfGlRqSI3FqE@n8SQaN48ND3mIzbhmfDVdDM0qVl3Q@6zw39Iw5hQWEW5mx2CCO0KLkNBEDKvoVxLqcxIAC91dUkNmIiqI2AaEaE4O3kiwgyv3CYYG@xIj/OdSLYJWRTrbpf2GGgeHk8Sb6yH6F/oncX7EJYnZq@A2ptuG44JgmnktY05Tu9MUJH/Aw "Jelly – Try It Online"

A monadic link taking a list of three positive integers and returning 1 if they are Borromean coprimes and 0 if not. TIO link checks all of the test cases.

## Explanation

```
ṭŒc        | Tag original list onto list of combinations of length 2
   g/€     | Reduce each list using GCD
      ċ1   | Count 1s
        =1 | = 1
```