Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

Heat

Sound

Music

Language

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

Growth

Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

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Sensors Sensings

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Faith, Love, Charity

Photosynthesis

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Systems

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Tools

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Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Select A Fruit

Container *A*, contains 7 apples. Container *B*, contains 7 peaches. You are asked to select a fruit from each of the following spaces formed by containers *A* and *B*:

(a) A ∪ (A ∩ B)

(b) A ∩ (A ∪ B)

(c) (A - B) ∪ B

What is the maximum number of apples you can select? What is the maximum number of peaches you can select?

Hint: simplify expressions before selecting. A ∪ B (fig. 7.87a) means the set of elements in A or in B or in both (if in both, counted only once). A ∩ B ( fig. 7.87b) means the set of elements in A and in B (elements common to both A and B). A - B (fig. 7.87c) means the set of elements in A but not in B.

**The string**:

S_{7}P_{6}A_{63} (Multi-Criteria Combination).
**The math**:

Pj Problem of Interest is of type *Grouping*. There are two groups of fruits (apples and peaches) from which to select. So this is a problem of type *multi-criteria grouping*.

(a) A ∪ (A ∩ B) = A. This is because there is no element common to both A and B.

So, A ∩ B = 0 and A ∪0 = A.

So, only apples will be selected because the space does not include peaches.

So, maximum number of apples you can select is 7.

(b) A ∩ (A ∪ B) = A. This is because A is the common space.

So, maximum number of apples you can select is 7. No peaches to be selected.

(c) (A - B) ∪ B = A ∪ B.

So, maximum number of apples you can select is 7 and
maximum number of peaches you can select is also 7.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Single Variable Functions

Conics

Ordinary Differential Equations (ODEs)

Vector Spaces

Real Numbers

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

More Pj Problem Strings