Answers & Hints for Selected Exercises 705
- (a) n(-n,n)=(-1,1) LJ (-n,n) = (-oo,+oo)
nEN nEN
u (-n, n)c = (-oo, -1] u [1, +oo) n (-n, n)c = 0
nEN nEN
(b) n ( -oo, n) = ( -oo, 1) U (-oo, n) = (-oo, +oo)
nEN nEN
LJ (-oo, n)c = [1, +oo) n (-oo,n)c =^0
nEN nEN
(c) n (-, ) = {O}
nEN
u (-*'*) = (-1,1)
nEN
c
U (-*, *t = (-oo, 0) U (0, +oo)
nEN
c
n (-*, *t = (-oo, -1] u [1, +oo)
nEN
(d) n [-2+*,2-*J=[-1,1J
nEN
u [-2 + * ,2-*] = (-2,2)
nEN
LJ [-2+*,2-*t=(-oo,-l)U(l,oo)
nEN
n [-2+ *,2-*t = (-oo,-2] u [2,oo)
nEN
(e) n (n , n + 1) = 0 U (n,n+l)=(l,+oo)-N
nEN nEN
n (n, n + l)c = (-oo, -1] UN
nEN
- XE ( LJ A,)c 9 X rf_ LJ A.x
.-\EA ,\EA
9 ,..., :L\ E A 3 x E A>. 9 '<! >. E A , x rf-A>.
9 '<!>.EA , x EA~ 9 x E n A~.
.-\EA
- x EB n ( LJ A>.) 9 x EB and x E LJ A>.
.-\EA .-\EA
9 x E B and 3>. E A 3 x E A>. 9 3>. E A 3 x E B and x E A>.
9 3>. EA 3 x EB n A,\ 9 x E u (B n A>.)·
.-\EA
EXERCISE SET B.2
- (a) V (f) =IR; R(f) =IR; 1-1; onto
(b) V (f) =IR; R(f) = [-2, oo); not 1-1; not onto
(c) V (f) = [~, oo); R(f) = [O, oo); 1-1; not onto
( d) V (f) =IR; R(f) = [O, oo ); not 1 -1; not onto
(e) V (f) =IR - {O}; R(f) = {-1, 1}; not 1-1; not onto
(f) V (f) =IR; R(f) = (0, 1); not 1-1; not onto
