Thread: Help with Discrete Maths Question.... stuck :(

Code:

Let S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Someone gives you six numbers  a1,....,a6 from S.
Let P = {{x, y} | x, y  ΠS and x + y = 15}

If f: {a1,...,a6} -> P is defined by f(ai) equals the set containing ai, explain
why f is not one-one.

If ai != (does not eqaul) aj but f(ai) = f(aj) show that ai + aj = 15.

Explain why, if 6 numbers are chosen from S then the sum of some pair of them
is 15.

Can someone help me

Cheers

Originally Posted by Privoxy

Code:

Let S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Someone gives you six numbers  a1,....,a6 from S.
Let P = {{x, y} | x, y  ΠS and x + y = 15}

If f: {a1,...,a6} -> P is defined by f(ai) equals the set containing ai, explain
why f is not one-one.

If ai != (does not eqaul) aj but f(ai) = f(aj) show that ai + aj = 15.

Explain why, if 6 numbers are chosen from S then the sum of some pair of them
is 15.

Can someone help me

Cheers

Are you having trouble understanding the questions? Mainly it's just definitions, and for the last part the pidgeonhole principle.

For starters, I would recommend writing out the set explicitly. Also, one has to understand why

is defined by equals the set containing

is a correct definition of a function. By this I mean why for any there exists an (unordered) pair from such that and why such is unique.