By A. T. Berztiss and Werner Rheinboldt (Auth.)

ISBN-10: 0120935503

ISBN-13: 9780120935505

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**Example text**

Thus, if n = 3, there are 8 minterms and 8 maxterms. , x denote elements of B. ,x )= 2"- 1 2 n © v(q(t )) * min m=0 (where we have used an obvious abbreviation for representing a repeated © operation). x 2 n n n m m 53 2b. Boolean Functions and Forms Proof. We shall prove the theorem by induction on n. (i) n = 1. Since x @l=x[@l =x[@x = 1, x * 0 = x[ * 0 = x[ * x = 0, x * I = x © 0 = x *x = x ®x = x x\ * 1 = x\ © 0 = x\ *x[ = x[ @x[ = x[ i 1 x x t t x x x x l9 9 every a(x ) ultimately reduces to 1, 0, x or x .

4 (a) Show that if A c £ and C c £>, then A n C ^ B n D. 5 (a) Find ^ ( 4 ) and ^ ( £ ) , where ^ = { 0 } and B = {a,b c,d}. How many members does the power set of C = {a, 6, c, . . , z} have ? 6 (a) Let M be a set of J integers and N a set of K integers (J, K ^ 1,000). Assume that elements of M and TV are stored in ascending order in locations M ( l ) , M ( 2 ) , . . , M ( J ) , and N ( l ) , N ( 2 ) , . . , N ( K ) , respectively. Write a subroutine for finding M KJ N and M n N. 7 (b) For { ^ | / e / } , where / = { 1 , 2, .

Since / is on A, the function has m elements, and no other function from any subset of A can f f f f 2a. Functions 45 have a greater number of elements. Hence at most 1 jn of the mn elements of A x B can belong to a function from A. 4. ) is the restriction of/to C, written f\C. A function/is an extension of a function # if and only if g c / The composite of functions # and A, symbolized /z o is the set {

### Data Structures. Theory and Practice by A. T. Berztiss and Werner Rheinboldt (Auth.)

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