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**URGENT ! Mathematical Logic and Structures**

Hey guys, i need a HUGE favor, i need the resolution for this 5 questions, its a question of end this year my degree or stay one year just with a subject. Please I am begging, who knows the resolution please say me something.

Part 1: Mathematical Logic

2- Convert the formula into the prenex form: (square root of)x p(x,g) -> ( inverted E )y (square root of) z q (x,y)

3- Consider the language L with the symbol of equality and one array predicate symbol. Write the formula in this language which express “there exist exactly one x such that p(x) holds”

4- Verify, which any of the formulas ¬ A v B and ( A or B ) substituted for x makes the formula ( A -> x ) -> ( x -> B ) a tautology.

Part 2: Mathematical Structures

1 - find the subgroup of the group (Z, +, 0) generated by the set {20,25} .

2 - Describe the free object over a given set X on the constant Pos (of partially ordened sets and isotone maps)