Discrete Mathematics

Atomic propositions are defined as follows: p= it's raining today q= today I went basketball practice r= the basketball court where I practice is being renovated s= I went riding a motorbike t=I brought an umbrella There are also a number of statements as follows: 1. It didn't rain today. 2. Today I didn't go to basket practice and the basketball court where I practiced was being renovated. 3. I went basketball practice and I didn't go on a bike ride, if and only if it rained today. 4. I bring an umbrella or I go to basketball practice. 5. If I don't go basketball practice or the basketball court where I practice is being renovated then I don't go on a motorcycle ride. Question: a. Translate the five statements above to the logic formula of the proposition with the definition of the corresponding atomic proposition as defined above! b. Are the five statements consistent with each other? Explain why