By Merlyn J. Behr

Educational Press Inc. offers Merlyn J. Behr and Dale G. Jungst's basics of hassle-free arithmetic: quantity structures and Algebra, released in 1971

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**Extra info for Fundamentals of elementary mathematics ; number systems and algebra**

**Example text**

13. 8 illustrates the complement of X. 10 illustrate the relative complement of Y with respect to X when Y is, and is not, a subset of X, respectively. \IA the complement of A, denoted by -A, is the set of elements which are in the universal set but not in A. 0 Sym bolically, VA, -A = {xix E U and x $. A } ; that is, \Ix, x E (-A) if and only if x $. A. 13 Let the universal set be U = { l,2,3,4,5,6,7,8}. P = {l,2,3,7}, and Q = {2,7,8}. Then, the complement of P is the set - p = { 4,5,6,8}. The relative complement of Q with respect to P is the set P \ Q = { l,3}.

F. {0} E A. d. {0} C A. is sometimes of interest to know how many subsets a given set has. TheIt following illustration starts a pattern which should fead you to a c guess of the answer and suggests a scheme for writing all subsets of a set. 37 Subsets No. of elements Set No. of subsets A=0 B = {a} 0 0 l l 0,{a} 2 C = {a,h} 2 0,{a,h}, {a},{ b } 0,{a,b,c},{a}, {b}, {c}, {a,h), {a,c), {b,c} D = 3 {a,b,c} E = {<1,b,c,d} 4 4 8 0,{a,b,c,d ), { a }, {h }, { c } , { d } , {a,b}, . . {a,h,c}, . . , ?

See the region labeled 1 in the Venn diagram. ) Lin es 2 and 3 indicate that elements of the universal set which are not elements of A can either be elements of B or not elements of B (that is, in the Venn diagram an element not in the region labeled 1 can be either in the region labeled 2 or in the region labeled 3). 18. We leave to the reader the problem of drawing a Ven n diagram which "corresponds" to the table. /\. 8. for each of the following sets: b. B \ A. 2. What do the element the statement VA VB, tables in Exercise 1 suggest about the truth of A \ B = B \ A?