Question

What do you obtain when you apply the projection \({P_{2,3,5}}\) to the 5 -tuple \((a,b,c,d,e)\)?

Short answer

The resultant answer is \((b,c,e)\).

Step-by-step solution

Given data

The projection is given.

Concept of sets

The concept of set is a very basic one.

It is simple; yet, it suffices as the basis on which all abstract notions in mathematics can be built.\(A\)set is determined by its elements.

If\(A\)is a set, write\(x \in A\)to say that\(x\)is an element of\(A\).

Simplify the expression

The projection \({P_{{i_1},{i_2}, \ldots ,{i_m}}}\) maps an \(n\)-tuple to the \(m\)-tuple which contain only the \({i_1}\)st, \({i_2}\)nd,\( \ldots \) and \({a_{{i_m}}}\) th component of the \(n\) -tuple, \((a,b,c,d,e)\).

In this case, the projection is \({P_{2,3,5}}\), which means that only the 2nd, 3rd and 5th component are kept. Or in other words, the first and 4th component are removed from the \(n\)-tuple, \((b,c,e)\).