22 Set operations 13 49 Let Ai be the set of all nonempty bi

2.2 Set operations 13 49. Let Ai be the set of all nonempty bit strings (that is, bit strings of length at least one) of length not exceeding i Find UAi. 50. FindU Ai and n 1 Ai if for every positive integer i, a) A ti, i 1, i 2,...) b) Ai (0, il. c) A (0, i), that is, the set of real numbers x with 0

Solution

49. Ai=An = {1,2,3..n}

Ai = A1 = {1}

50.a) U Ai = {1, 2, 3, ... inf} the set of all positive integers without 0
Ai = Ø, the empty set, each successive set excludes 1 member of the previous set

b) U Ai = {0, 1, 2, ..., inf} the set of all positive integers with 0
Ai = {0}

c) U Ai = the positive real numbers without the integers or zero
Ai = Ø, the empty set

d) U Ai = (1, inf) the real numbers > 1
Ai = Ø, the empty set

52.Numbering the bits from left to right
Here are the 10 bits:
00000 00000
now if we want #5 in the set we change the 5th bit to a 1
00001 00000

Then do it for the others similarly.

12345 6789,10
00111 00000

1 23 456 789,10
1 01 001 0001