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2. Determine each of the following statement is true or false and justify your answer: (a) S has a subgroup of order 15...
TRUE/FALSE (5 points) Answer each of the following as True or False. You don't have to justify your answer. (a) The quotient group Z12/(8) is isomorphic to Za (b) Any subgroup H of G of index 2 is normal in G. (c) For every n 2 2, the quotient group Sn/An is isomorphic to Z2. (d) If H is a normal subgroup of G, then Ha-1H for every a E H (e) The symmetric group S3 has exactly three normal...
Discrete mathematics Determine if the following statement is true or false. Justify your answer If a = b (mod n) then a^3 = b^3 (mod n)
9. Mark the statement True or False. Justify your answer. (7 points each) (a) If S and T are compact sets, then S T is also compact. (b) There exists a set S which is not compact, but T = {?: ES) is compact
6. (15) Determine whether each statement is true or false. Justify your answers. (a) if f(n) = O(g(n)), then g(n) = O(f(n)). (b) if f(n) = O(g(n)), then g(n) = Ω(f(n)). (c) if f(n) = Θ(g(n)), then g(n) = Θ(f(n)).
Determine whether each statement is True or False. Justify each answer a. A vector is any element of a vector space. Is this statement true or false? O A. False; a vector space is any element of a vector O B. True by the definition of a vector space O C. False; not all vectors are elements of a vector space. b. If u is a vector in a vector space V, then (-1)u is the same as the negative...
Determine whether the following statement is true or false. Justify your answer. Let a and b be real numbers. The following system of equations can have exactly two solutions. 2x+7y=9 3x-4y=b
We know that |S5| = 120 = 8 × 15, so a Sylow 2-subgroup of S5 has order 8. (a) Find an example of a Sylow 2-subgroup of S5. (b) Is this Sylow subgroup abelian? (c) Can you identify this Sylow subgroup with some other well known group of order 8? (d) Calculate n2(S5).
Determine if the statement is true or false, and justify your answer. If u1, u2, u3 is linearly independent, then so is (ui, u2. u3. u4) True. If u1. u2, u3ł is linearly independent, then the equation xu1 + xzu2 + x3u3 0 has a nontrivial solution, and therefore so does x1U + xzu2 x3u3 False. Consider for example u1 = 0 False. Consider for example u4 = 0. True. The echelon form of the augmented matrix [u1 u2 u3...
2. [2 marks] [2 marks] (a) Is the following statement true or false? Justify your answer. "A use case diagram describes a sequence of use cases representing the behaviour of the system when interacting with its environment (i.e., the actors)." (b) Is the following statement true or false? Justify your answer. "Structural models display the organisation of a system in terms of what the system does." (c) Is the following statement true or false? Justify your answer. "A good design...
2. Mark each statement True or False. Justify your answer. (6 points each) (a) (A\B) U ( BA) = (AUB) (ANB). (m) º (7.1+5) = (a :) n=2 1 3. Let A = {J,Q,K) and B = {4,0}. Find (list thc clements of) the set A x B. Find |A x B) and P(A x B) (9 points) 3