Bitten off more than I can chew..?

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So, you want the output pin to go HIGH when there is ANY input? There will ALWAYS be input from the temperature and humidity sensor, so you can skip reading them.

const byte relayPin = 2; // Change to whatever pin the relay is connected to

void setup()
{
   pinMode(relayPin, OUTPUT);

   digitalWrite(relayPin, LOW); // Change to HIGH is LOW doesn't activate the relay
}

void loop()
{
   // Nothing to do here, since there would ALWAYS be input, so the relay would always be on
}

That code meets your stated requirements. You owe me a beer.