14 SETS Chapter 1
B = {x E Rlsin zx = 0)
C= {x€R(x2= -1) (d) D={x~RIx~-5x+7<0)
E = {XE RI10x2 - 7x - 12 20) (f) F = {x~R1(6x - 81 < 4)
G = {X ERI~~x - 121 < 0) (h) H = {xER)~~x+ 13) 50)
I = {XERIX >O and cosxx =cotzx)
J = {x E Rlsec x/(cos x + tan x) = sin x)
K = {x E RI(2x + 7)lI2 is a real number)
L= {xEQ~x~+(~-&)x+~&=o)
M = {z E C (ZZ* = (zI2) *(n) N= {z~C(Im(z)=0}
(Note: If a and b are real numbers and z = a + bi, then b is called the imaginary
part of z, denoted Im (z), z* = a - bi is called the complex conjugate of z, and lzl =
(a2 + b2)'I2 is called the modulus of z.)
- (a) Which of the following descriptions of sets are well defined?
(i) (r 1s is an American citizen on July 4, 1976)
- (i) {X I x is the 21 71 st digit in the decimal expansion of J3)
- (iii) {xlx is an honest man)
(iv) {xlx is a month whose name in the English language ends in the letter r)
(v) (XIX is a day in the middle of the week)
(vi) (x (sin 2.u)
(vii) {x E N 1 x is an integral multiple of 4)
(viii) {x I x is an aardling}
(ix) {xJ((x2 - 6x + 3)/(x3 + 4))1'2}
(x) {x~~lx+y=4) I
(b) For each of the sets in (a) that is well defined, suggest an appropriate universal
set.
- Given the following "pattern" descriptions of infinite sets, list five additional ele-
ments of each: '1
(a) A = {I,& $,.. .) (b) B={l,2,3,5,8,13 ,...)
*(c) C={-l,2, -4,8 ,...) (d) D = {~,4~,7n, 1071,... )
(e) E= { ...,. -8, -5, -2,1,4,7) (f) F = {... , -8, -5, -2, 1,4,7,.. .)
- Given the following six sets, answer true or false to statements (a) through (n):
(a) -~EA
(c) D c C
(e) D c C
ts) DEE
(i) - 6 E F
(k) +&F
(m) 0 E B
(b) 6 E B
(d) C G D
(f) E E D
(h) -~EA
(1) --YEA
(1) 100EB
(n) - 1 4 D
