If I do not rollerblade, then i go to the gym

If i ride my bike and I go to the gym, then i am tired

I am not tired

I ride my bike

Let R=I rollerblade

Let G=I go to the gym

Let B= I ride my bike

Let T= I am tired

The correct logic connectors are

~R->G

(B^G)->T

~T

B

Prove:R

**Subject Mathematics Math Logic**