Question

Let A = {3, 4, 6} and B = {x, y}. Let p1 and p2 be the projections of A × B onto the first and second coordinates. For each pair (a, b) ∈ A × B, p1(a, b) = a, and p2(a, b) = b.

a) Linear algebra concepts
b) Set theory and projections
c) Cartesian product analysis
d) Algebraic structures in mathematics

Answer 1

This question pertains to the mathematical concepts of set theory Cartesian products, projections, as well as linear algebra involving dot and cross products of vectors.

Step-by-step explanation:

The question falls under the subject of Mathematics, specifically related to linear algebra, set theory, and vector analysis. In set theory, the Cartesian product A × B is the set of all possible ordered pairs where the first element is from set A and the second is from set B. The projections p1 and p2 are functions that return respectively the first and second components of each ordered pair in the product. In linear algebra, when dealing with vectors, terms like scalar product (dot product) and vector product (cross product) come into play. The dot product of two vectors can be visualized as projecting one vector onto the direction of another and multiplying it by the magnitude of the other vector. The cross product results in a vector that is perpendicular to the plane containing the original vectors, providing information about their directional relation. It is important to distinguish the set theory concept of Cartesian products and projections from the linear algebra concept of dot and cross products of vectors, despite the similar language and notation.