Homework Help: Math: Arithmetic: Postulates

Postulates of Equality

1. Reflexive Property of Equality: a = a
2. Symmetric Property of Equality: if a = b, then b = a
3. Transitive Property of Equality: if a = b and b = c, then a = c

Postulates of Equality and Operations

1. Addition Property of Equality: if a = b, then a + c = b + c
2. Multiplication Property of Equality: if a = b, then a * c = b * c
3. Substitution Property of Equality: if a = b, then a can be substituted for b in any equation or inequality
4. Subtraction Property of Equality: if a = b, then a - c = b - c

Postulates of Inequality and Operations

1. Addition Property of Inequality: if a < > b, then a + c < > b + c
2. Multiplication Property of Inequality: if a < b and c > 0, then a * c < b * c
if a < b and c < 0, then a * c > b * c
3. Equation to Inequality Property: if a and b are positive, and a + b = c, then c > a and c > b
if a and b are negative, and a + b = c, then c < a and c < b
4. Subtraction Property of Inequality: if a < > b, then a - c < > b - c
5. Transitive Property of Inequality: if a < b and b < c, then a < c

Postulates of Operation

1. Commutative Property of Addition: a + b = b + a
2. Commutative Property of Multiplication: a * b = b * a
3. Distributive Property: a * (b + c) = a * b + a * c and vice versa

Homework Help: Math: Arithmetic

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