Exercise D

Using the symbolization key given, translate each English-language sentence into TFL.

• $J_{1}$:

  John Coltrane played tenor sax

• $J_{2}$:

  John Coltrane played soprano sax

• $J_{3}$:

  John Coltrane played tuba

• $M_{1}$:

  Miles Davis played trumpet

• $M_{2}$:

  Miles Davis played tuba

1. John Coltrane played tenor and soprano sax.

3. Neither Miles Davis nor John Coltrane played tuba.

5. John Coltrane did not play both tenor sax and tuba.

7. John Coltrane did not play tenor sax unless he also played soprano sax.

9. John Coltrane did not play tuba, but Miles Davis did.

11. Miles Davis played trumpet only if he also played tuba.

13. If Miles Davis played trumpet, then John Coltrane played at least one of these three instruments: tenor sax, soprano sax, or tuba.

15. If John Coltrane played tuba then Miles Davis played neither trumpet nor tuba.

17. Miles Davis and John Coltrane both played tuba if and only if Coltrane did not play tenor sax and Miles Davis did not play trumpet.