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

1. ## 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  Œ S 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

2. 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  Œ S 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.

3. For starters, I would recommend writing out the set $P$ explicitly. Also, one has to understand why
$f: \{a_1,...,a_6\}\to P$ is defi ned by $f(a_i)$ equals the set containing $\displaystyle a_i$
is a correct definition of a function. By this I mean why for any $a_i$ there exists an (unordered) pair $p$ from $P$ such that $a_i\in p$ and why such $p$ is unique.