6. Let S be a k-element subset of {1,...,n}. Prove that, if () >n-1, then there exists a, b, X, Y ES such that a + b, {a,b} + {x,y} and b - a=y- 2. (Note that it may be the case that b= x or a = y.) 7. Let S be a k-element subset of {1,...,n}. Prove that, if [k/2] [k/2] > n - 1, then there exists a 4-element subset {a,b, x, y} CS such that a b = x - y. (Unlike the previous question, a, b, x, y must be 4 distinct elements.)