Homework Answers
A functional completeness may be defined as a set of logical connectives Or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression. A well-known complete set of connectives is {AND, NOT}, consisting of binary conjunction and negation. Each of the singleton sets {NAND} and {NOR} is functionally complete.
A gate Or set of gates which is functionally complete can be called a universal gates.
In logic, typically take as premitive some subset text of connectives; conjunction, disjunction, negation, material conditional.
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(11) (3+3+5+5+ 2) Define functional completeness. Show that x + y = (x + y) +...
(5 pts each) Give example of an explicit function f in each of the following category...
(5 pts each) Give example of an explicit function f in each of the following category with properly written domain D and range R such that (a) There exists a subset S of D with f-'[F(S)] + S (b) There exists a subset T of R with f[f-(T)] #T (11) (3+3+ 5 + 5 + 2) Define functional completeness. Show that x + y = (x + y) + (x + y), x · y = (x + x) +...
(3 pts each) For each of the following find an indexed collection {An}nen of distinct sets...
(3 pts each) For each of the following find an indexed collection {An}nen of distinct sets (no two sets are equal) such that (a) n=1 An = {0} (b) Un=1 An = [0, 1] (c) n=1 An = {-1,0,1} (5 pts each) Give example of an explicit function f in each of the following category with properly written domain D and range R such that (a) There exists a subset S of D with f-'[F(S)] + S (b) There exists...
(5 pts) Give an example of a relation on a set that is a) both symmetric...
(5 pts) Give an example of a relation on a set that is a) both symmetric and antisymmetric. b) neither symmetric nor antisymmetric. (3 pts each) For each of the following find an indexed collection {An}nen of distinct sets (no two sets are equal) such that (a) n =1 An = {0} (b) Um_1 An = [0, 1] (c) n =1 An = {-1,0,1} (5 pts each) Give example of an explicit function f in each of the following category...
2. Define f : RR by - y 1(x) = { "2+2 (ay) (0,0); (z,y) =...
2. Define f : RR by - y 1(x) = { "2+2 (ay) (0,0); (z,y) = (0,0). (i) Isf continuous at (0,0)? Justify your answer. (ii) Show that Daf(3,0) = x for all x and D.f(0,y) = -y for all y (iii) D2f(0,0) + D2,1f(0,0). (iv) Is f differentiable at (0,0)? Justify your answer.
Question 3. Let 3 5/' and for x(2),y -(,) ER2 define (a) Show that the assignment (x, y) > (x,y) defined ın (1) us an nner product [10 marks (b) If a - (1,-1) and b - (1,1), then show that the...
Question 3. Let 3 5/' and for x(2),y -(,) ER2 define (a) Show that the assignment (x, y) > (x,y) defined ın (1) us an nner product [10 marks (b) If a - (1,-1) and b - (1,1), then show that the vectors a and b are lınearly ndependent but they are not orthogonal with respect to the inner product n (1) 3 marks] (c) Given the vectors a and b in (b), the set (a, by is hence a...
8) Is the point (-5, 3) on the circle defined by (x - 2)2 + (y...
8) Is the point (-5, 3) on the circle defined by (x - 2)2 + (y + 1)2 = 64? Justify your answer! A) No B) Yes
Define the purpose of the following objectives 5 Occurrence 2 pt each 6 Completeness 7 Posting...
Define the purpose of the following objectives 5 Occurrence 2 pt each 6 Completeness 7 Posting and summarization
2. Given R(x,y, z, w, k, t). There are two keys: (x,y) and z. Given the...
2. Given R(x,y, z, w, k, t). There are two keys: (x,y) and z. Given the following functional dependency: F = { {x,y} {z,w,k,t}, z {x,y,w,k,t }, yt}. Is R in 2nd normal form? Justify your answer. 3. Given R(x,y, z, w, k, t). There are two keys: (x,y) and z. Given the following functional dependency: F = { fd1:{x,y} {z,w,k,t}, fd2: z {x,y,w,k,t }, fd3:k x}. Is R in 3rd normal form? Justify your answer....
Explain the evaluation of the following Scheme code: (define x 10) (define y 11) (define proc2...
Explain the evaluation of the following Scheme code: (define x 10) (define y 11) (define proc2 (lambda () (cons x (cons y '())))) (define proc1 (lambda (x y) (proc2))) (define main (lambda () (cond ((zero? (read)) (proc1 5 20)) (else (proc2))))) (main)
a - e (a) X + y +z = 11 X – Y – 2= -3...
a - e
(a) X + y +z = 11 X – Y – 2= -3 -2 + y - 2 = 5 (3x – y + 2z = 2 (b) x+y+z+t+p=17 X - Y - 2-t-p= -5 z +t+ p + y = 11 p - x - y = 1 -t + x = 10 (c) x +y + 2+t= -6 X - Y - 2 -t = 20 y - X=-39 2x + 3t + y -...
(5 pts each) Give example of an explicit function f in each of the following category with properly written domain D and range R such that (a) There exists a subset S of D with f-'[F(S)] + S (b) There exists a subset T of R with f[f-(T)] #T (11) (3+3+ 5 + 5 + 2) Define functional completeness. Show that x + y = (x + y) + (x + y), x · y = (x + x) +...
(3 pts each) For each of the following find an indexed collection {An}nen of distinct sets (no two sets are equal) such that (a) n=1 An = {0} (b) Un=1 An = [0, 1] (c) n=1 An = {-1,0,1} (5 pts each) Give example of an explicit function f in each of the following category with properly written domain D and range R such that (a) There exists a subset S of D with f-'[F(S)] + S (b) There exists...
(5 pts) Give an example of a relation on a set that is a) both symmetric and antisymmetric. b) neither symmetric nor antisymmetric. (3 pts each) For each of the following find an indexed collection {An}nen of distinct sets (no two sets are equal) such that (a) n =1 An = {0} (b) Um_1 An = [0, 1] (c) n =1 An = {-1,0,1} (5 pts each) Give example of an explicit function f in each of the following category...
2. Define f : RR by - y 1(x) = { "2+2 (ay) (0,0); (z,y) = (0,0). (i) Isf continuous at (0,0)? Justify your answer. (ii) Show that Daf(3,0) = x for all x and D.f(0,y) = -y for all y (iii) D2f(0,0) + D2,1f(0,0). (iv) Is f differentiable at (0,0)? Justify your answer.
Question 3. Let 3 5/' and for x(2),y -(,) ER2 define (a) Show that the assignment (x, y) > (x,y) defined ın (1) us an nner product [10 marks (b) If a - (1,-1) and b - (1,1), then show that the vectors a and b are lınearly ndependent but they are not orthogonal with respect to the inner product n (1) 3 marks] (c) Given the vectors a and b in (b), the set (a, by is hence a...
8) Is the point (-5, 3) on the circle defined by (x - 2)2 + (y + 1)2 = 64? Justify your answer! A) No B) Yes
Define the purpose of the following objectives 5 Occurrence 2 pt each 6 Completeness 7 Posting and summarization
Explain the evaluation of the following Scheme code: (define x 10) (define y 11) (define proc2 (lambda () (cons x (cons y '())))) (define proc1 (lambda (x y) (proc2))) (define main (lambda () (cond ((zero? (read)) (proc1 5 20)) (else (proc2))))) (main)
a - e
(a) X + y +z = 11 X – Y – 2= -3 -2 + y - 2 = 5 (3x – y + 2z = 2 (b) x+y+z+t+p=17 X - Y - 2-t-p= -5 z +t+ p + y = 11 p - x - y = 1 -t + x = 10 (c) x +y + 2+t= -6 X - Y - 2 -t = 20 y - X=-39 2x + 3t + y -...
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