# n-ary relations and their applications

• Jun 7th 2008, 02:14 PM
robocop_911
n-ary relations and their applications
Can anybody do the following problem?
I don't know how to go about doing it...

Give an example to show that if R and S are both n-ary relations, then

$
P_{i_1,i_2,...,i_m}(R \cap S)$
may be different from $
P_{i_1,i_2,...,i_m}(R) \cap P_{i_1,i_2,...,i_m}(S)$
• Jun 7th 2008, 02:31 PM
Plato
Quote:

Originally Posted by robocop_911
Give an example to show that if R and S are both n-ary relations, then $
P_{i_1,i_2,...,i_m}(R \cap S)$
may be different from $
P_{i_1,i_2,...,i_m}(R) \cap P_{i_1,i_2,...,i_m}(S)$

How does your text define $P_{i_1,i_2,...,i_m}(S)$?
• Jun 7th 2008, 02:46 PM
robocop_911
Quote:

Originally Posted by Plato
How does your text define $P_{i_1,i_2,...,i_m}(S)$?

The projection $P_{i_1,i_2,...,i_m}$ where $i_1 < i_2 < ... < i_m$, maps the n-tuple $(a_1, a_2,..., a_n)$ to the m-tuple $(a_{i_1}, a_{i_2}, ..., a_{i_m})$, where m <= n.

In other words, the projection P_i1, i_2,..., i_m deletes $n-m$ of the components of an n-tuple, levaing the i1th, i2th and imth components.
• Jun 7th 2008, 02:57 PM
robocop_911
Quote:

Originally Posted by robocop_911
The projection $P_{i_1,i_2,...,i_m}$ where $i_1 < i_2 < ... < i_m$, maps the n-tuple $(a_1, a_2,..., a_n)$ to the m-tuple $(a_{i_1}, a_{i_2}, ..., a_{i_m})$, where m <= n.

In other words, the projection P_i1, i_2,..., i_m deletes $n-m$ of the components of an n-tuple, levaing the i1th, i2th and imth components.

For example:
If $P_{1,3}$ is applied to a 4 tuple (2,3,0,4) gives (2,0)