FINITE SETS AND THE COUNTING PRINCIPLE 1.39 Determine which of the following set
ID: 3195132 • Letter: F
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FINITE SETS AND THE COUNTING PRINCIPLE 1.39 Determine which of the following sets are finite: (a) Lines parallel to the x axis. (c) Integers which are multiples of s. (b) Letters in the English alphabet. (d) Animals living on the carth. 140 Use Theorem 1.9 to prove Corollary 1.10: Suppose A, B, C are finite sets. Then AUBUCis finite and A survcy on a sample of 25 new cars being sold at a local auto deaker was conducted to see which of three popular options, air conditioning (A), radio (R), and power windows (W), were already installed. The survey found: 1-41 15 had air-conditioning (A). 5 lad A and P 12 had raddio (R), 11 had power windows (W. 4 had R and W 9 had A and R,h 3 had all three options. Tind the numherof cars that hud: (a)only w b)only A: (c)only R, d) R and W but not A: e)Aand Rbuto W (f) only one of the options; (g) at least onc option. (h) none of the options. CLASSES OF SETS 1.42 Find the power set P(A) of { ', 23, 4, 5]. (a) Lnst the elements of A. (b) Find n(A). e Find the power set of A. 1.44 Suppose A ts finte and n(A) m. Prove lhe power seuP(A) has 2m lemcalg, PARTITIONS 145 Les1.2.8. 21. Duermime whether or not each of the following is a paritbon of 5 a) I{1, 3, 61,128]. I5,7, 9] 1 (b) [ { t, 5,7], {2, 4, 8,')], {3, 5,61 1 Let S (c) [12,4, 5,8h ll,13,6. T11 (d) II 1, 2, 73, 51, 14,6, 8, 9. I 3,51 46 1, 2, 3 4, 5, 6]. Denenn n whether or BOL each of the following is aparut no S b r-un21. 13.5.611 o P-IIL,35).24.6.71 1.47 Deienuinc whether or not cach of the following is a partition of the set Nof posilive inirgersExplanation / Answer
Solution 1.39
(a) There can be infinite number of lines parellel to x axis thus number of set elements would be infinite and it makes set infinite.
(b)There are infite multiple integers of 5 like 5,10,15,20.... thus number of set elements would be infinite and it makes set infinite.
(c) There are only 26 alphabets of english. Thus this is example of finite set.
(d) There are infinite numbers of animals living on earth thus number of set elements would be infinite and it makes set infinite.
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