Question 4: Let G be a finite abelian group of order o(G) and suppose the integer n is relatively prime to o(G). Consider the mapping : G→G defined by (y) = y". Prove that this mapping is an automorphism.

Question 5: Let G be a group, o an automorphism of G, N a normal subgroup of G. Prove that (N) is a normal subgroup of G.

Question 2: Let A(G) be the set of all automorphisms of a group G. Prove that if G is a group having only two elements, then A(G) consists only of I.

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Theorem Let E be a subset of a space X then- E = EVE = E'V LCE).

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CHAPTER 1: HISTORY OF COOPERATIVES AND STATE POLICIES Questions for Critical Thinking 1. Discuss the different stages in the history of the Philippine cooperative movement 2. What do you think is meant when it is stated that "one cause for the failure of cooperatives is due to non-patronage by coop members? 3. When the principle of subsidiarity is followed, what are the different manifestations of this principle? Explain. 4. Cooperatives can promote social justice in Philippine society according to the declared policy of the state on cooperatives. Why and how? 5. Why is the recognition of the nature of man neccessary in the success of the cooperative movement? 6. The interest on capital in coops is limited but there is no such limitation in corporation. Explain. 7. How is government intervention proscribed in the declared policies of the government under the present Cooperative Code. 8. Cooperatives grant patronage refund, which is not present in corporations. How do you explain this…

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T1 T₂ T7 T11 (15) (18) 8 (12) (60) 5 T3 T6 12° 5 5 5 T8 T10 T4 (25) T5 To 1. List all the maximal paths and their weights for the graph above. 2. Give the decreasing-time priority list. 3. Schedule the project using 2 processors and the decreasing-time priority list.