Supplement to the Classical Algebra text

ANSWERS

to the odd numbered Exercises and Problems in the Supplement

EXERCISE SET 0


1.  True statement
3.  Not a statement
5.  Not a statement
7. 
P NOT ( NOT P )
T
F 		T
F

9. 
P Q R P => ( Q OR R )
T
T
T
T
F
F
F
F 		T
T
F
F
T
T
F
F 		T
F
T
F
T
F
T
F 		T
T
T
F
T
T
T
T

11. 
P Q R ( P OR NOT Q ) => R
T
T
T
T
F
F
F
F 		T
T
F
F
T
T
F
F 		T
F
T
F
T
F
T
F 		T
F
T
F
T
T
T
F

15. 
P Q P NOR Q
T
T
F
F 		T
F
T
F 		F
F
F
T

17.  Q => P
19.  P => Q
21.  P <=> Q
25.  P => Q
27.  Q AND NOT P
29.  If I have broken my leg then I cannot walk.
31.  If I take the bus then I have broken my leg or I cannot walk.
33.  exists x  forall y   x =< y ;  integers
35.  exists x  forall y   forall z   x > y z ;  integers
37.  exists x ( NOT P(x) AND NOT Q(x) )
39.  forall x  ( P(x) AND NOT Q(x) )
41.  Every real number is as large as any real number. False
43.  There is a smallest real number. False
45.  Equivalent
47.  Not equivalent
49.  exists x  ( ( xinA ) AND ( xinB ) AND ( x is not in C) )
51.  exists epsilon>0   forall delta>0   exists x    ( 0 < | x - a | < delta AND | f(x) - L | >=epsilon)
57.  If  x2 =< 9  then  x =< 3.
59.  If a number is prime then it is not divisible by 2.

PROBLEM SET 3


79.  xn xn-1 ... x1 x1
81.  x1 - 2 x2 + 4 x3 + ... + (-2)n-1 xn
83.  e(0) = 1; e(n) = e(n - 1) + ( 1 / n! ) for n > 0
© 1998 William J. Gilbert and Scott A. Vanstone, University of Waterloo

Supplement Contents