Question 2 please Exercise 1. Define an operation on Z by a b= a - b. Determine ife is associative or commutative. Find a right identity. Is there a left identity? What about inverses? Exercise 2. Write a multiplication table for the set A = {a,b,c,d,e} such that e is an identity element, the product is defined for all elements and each element has an inverse, but the product is NOT associative. Show by example that it is not associative....
3. Let G be a group containing 6 elements a, b, c, d, e, and f. Under the group operation called the multiplication, we know that ad = c, bd = f, and f2 = bc = e. We showed you in class that the identity is e, hence the e-row and e-column were revealed. Using associativity, we also found cb, cf, af, and a2. Now try to imitate the idea and find five more entries. Justify your answer. Hint:...
1. Let G be element. Consider the subgroups H = <a) = { a, b, c, d, e} and K = (j)-{ e, j, o, t} the group whose Cayley diagram is shown below, and suppose e is the identity rl Carry out the following steps for both of these subgroups. Let the cosets element-wise. (e) Write G as a disjoint union of the subgroup's left cosets. (b) Write G as a disjoint union of the subgroup's right cosets. (c)...
1- (2,5+2,5 mark) Consider in GL(2, Q), the subset (a=1 or a=-1),bez Prove that H, with multiplication, is a subgroup of GL(2,Q) a) Is the function b) an homomorphism of groups? Justify your answer 2 (3 marks) Let G be a group and a E G an element of order 12. Find the orders of each of the elements of (a) 3- (1+1,5 marks) Let G be a group such that any non-identity element has order 2. Prove that a)...
Again, suppose we have a relation on attributes A, B, C, D, E, and F, and these functional dependencies hold: S = { B → DE, BF → C, CF → B, DF → AE }. (a) Does it follow from S that B → A? (b) Does it follow from S that CF → E? (c) Does it follow from S that DF → B? (d) Does it follow from S that BD → C? (e) Does it follow...
5. (3, 4, 3 points) Let A-a, b, c, d, e, f, g (a) how many closed binary operations f on A satisfy Aa, b)tc b) How many closed binary operations f on A have an identity and a, b)-c? (c) How many fin (b) are commutative? 6. 10 points) Suppose that R and R are equivalent relations on the set S. Determine whether each of the following combinations of R and R2 must be an equivalent relation. (a) R1...
Let R(A, B, C, D) be a relation with FDs F= {A->B, A->C, C->A, B->C, ABC->D} which of the statement is correct? Question 2 Not yet answered Marked out of 2.00 P Flag question Let R(A,B,C,D) be a relation with FDs F = {AL-B, AC, CA, B-C, ABC-D} Which of the following statements is correct ? (2 Points) Select one: O G = {A--B, BC, C-A, AC-D} is a canonical cover of F OH = {A-C, C+A, B-C, B-D} is...
which part b uses the answer from part a. 4. (35 pts) Let f(x) = x(1-x) for 0 < x < 1. (a) (15 pts) Compute the Fourier cosine series FCS f(x). (b) (5 pta) Find the formal solution of the problem BC u,(O, t)-u(1,t)-0, (c) (5 pts) Show that there can be no solution of problem (A) which is Ca for 0 S S 1 and (d) (10 pts) Show that there is a Co solution of the DE...
Let R(A,B,C,D) be a relation with FDs F = {A—B, AC, C-A, B,C, ABC-D} Which of the following statements is correct ? (2 points) Select one: G = {A-B, B-C, C-A, AC=D } is a canonical cover of F H = { AC, CA, BC,BD} is a canonical cover of F. o F is a canonical cover of itself. O G and H are canonical covers of F. None of the above.
Let A, B, C be three collinear points and let D, E, F be the midpoints of segments AB, BC, and AC, respectively. Prove that the segments DE and BF have the same midpoint. Let d be a line and let A, B, C be three points not on d. Prove that if d does not separate points A and B and it does not separate points B and C, then it does not separate points A and C.