Solutions to Exercises for Section 5.3

2. The scope of ‘$x’ is ‘Ax Ú ~Bx’

3. The scope of ‘$z’ is ‘Ax’

4. The scope of ‘"x’ is ‘Ax’

6. The scope of ‘"x’ is ‘Gx ® $x$zFxyz’

The scope of ‘$x’ is ‘$zFxyz’

The scope of ‘$z’ is ‘Fxyz’

7. The scope of ‘$y’ is ‘Mx’

8. The scope of ‘"x’ is ‘$y(Axy & Px)’

The scope of ‘$y’ is ‘Axy & Px’

9. The scope of ‘$x’ is ‘(Ax & (C Ú Ay))’

10. The scope of ‘"x’ is ‘Cxy’

11. The scope of ‘$x’ is ‘Px & Bxa’

12. The scope of ‘"z’ is ‘Laz’

The scope of ‘$y’ is ‘Mya’

13. In ‘~AxAx’, the second occurrence of ‘x’ is a bound occurrence.

14. In ‘"x$y(Az & Bya)’, the occurrence of ‘z’ is a free occurrence, and the second

occurrence of ‘y’ is a bound occurrence.

16. In ‘Bx Ú $xAxx’, the first occurrence of ‘x’ is a free occurrence, the third occurrence of

‘x’ is a bound occurrence, and the fourth occurrence of ‘x’ is a bound occurrence.

17. In ‘"x(Ax ® (Pb Ú Px))’, the second occurrence of ‘x’ is a bound occurrence, as is the

third occurrence of ‘x’.

18. In ‘$zAz Ú "yAy’, the second occurrence of ‘z’ is a bound occurrence, and the second

occurrence of ‘y’ is a bound occurrence.

20. In ‘$y(~By ↔ (~Axz Ú Cy))’, the second occurrence of ‘y’ is a bound occurrence, the

first occurrence of ‘x’ is a free occurrence, the first occurrence of ‘z’ is a free occurrence, and

the third occurrence of ‘y’ is a bound occurrence.

21. In ‘"xAbx’, the second occurrence of ‘x’ is a bound occurrence.

40. General

41. Simple

42. General

44. General

45. Simple

46. General

47. Compound

48. Compound

50. General