大家好，在学经济数学，但都是英文的不太理解，谁能帮忙用中文解一下下面几道题，再加点大概意思。

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1. Let G be a group of people. Assume that for every person A in G,there is a person B in G such that A knows a friend of B.
Is it true that for every person B in G, there is aperson A in G such that B knows a friend of A? Explain.

2. The symmetric difference operator △ on set A and B is defined as

A△B = (A\B)∪(B\A);

which defines theset of all elements that belong to exactly either A or B.

(a) Show that if A = B, then A△B =Ø

(b) Show thefollowing properties are held

(i) A△B = B△A (commutative)

(ii) (A△B) △C = A△(B△C) (associative)

(iii) A△; Ø= A

3. An operation α on a set A is defined to be afunction of the Cartesian product A × A into A, i.e.,

α: A × A ⇒ A

Let α: N × N ⇒ N be the operation of least common multiple(l.c.m.). That is, α (a, b) ≡ a · b = l.c.m. of a and b.

(a) Is α commutative?

(b) Is α associative?

(c) Find theidentity element of α.

(d) Which elementin N, if any, have inverses and what are they?