Read the following instructions carefully and apply those in your translation:
interpreting the statement indicator h as i am happy
interpreting the statement indicator t as i am troubled
let connective indicator & substitute the connective and
let connective indicator v substitute the connective or
let connective indicator ~ substitute the connective not
let connective indicator → substitute the connective if-then
let connective indicator ↔ substitute the connective if-and-only-if.
translate the following statements:
exercise #1. i am happy.
exercise #2. i am not happy.
exercise #3. i am troubled.
exercise #4. i am not troubled.
exercise #5. i am happy or i am troubled.
exercise #6. it is not both the case that i am happy and troubled.
exercise #7. if i am not happy, then i am troubled.
exercise #8. it is not the case that if i am happy, then i am troubled.
exercise #9. i am happy if and only if i am not troubled.
exercise #10. ~ (h v t)
exercise #11. ~ t → h
exercise #12. ~ h & ~ t