Mastering MySQL Database Architecture: Deep Dive into MySQL Shell and MySQL R...
2 2 published
1. 4210 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1
2-2 Properties from Algebra
Please write down the properties
on these slides so that we may
discuss them and use them
tomorrow.
2. 421
0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1
Properties to Know
• When in the “number world” we can use the
real number properties from Algebra.
• The Properties of Equality that we will use
most often are:
3. 421
0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1
• Addition Property If a = b and c = d, then
a + c = b + d.
• Subtraction Property If a = b and c = d, then
a c = b d.
• Multiplication Property If a = b, then ca = cb.
• Division Property If a = b and c 0, then
• Substitution Property If a = b, then either a or b
may be substituted for the
other in any equation (or
inequality).
Properties from Algebra
.
a b
c c
4. 421
0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1
More Properties of Algebra
• Reflexive Property a = a
• Symmetric Property If a = b, then b = a.
• Transitive Property If a = b and b = c, then
a = c.
5. 421
0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1
The Distributive Property
For the real number system:
• a(b + c) = ab + ac
• (a + b)c = ac + bc
Solve 3x = 6 – ½x and justify each step.
7. 421
0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1
Take Note:
• There is NO Substitution Property of
Congruence!
• To use the Substitution Property, you
MUST be in the “number world.”