If a = b, then a - c = b - c Subtraction Property of Equality Distributive Property Addition Property of Equality Multiplication Property of Equality

Subtraction Property of Equality

If a = b, then ac = bc Associative Property for Multiplication Transitive Property of Equality Multiplication Property of Equality Addition Property of Equality

Multiplication Property of Equality

If a = b & b = c, then a = c Communitive Property for Addition Symmetric Property of Equality Communitive Property for Multiplication Transitive Property of Equality

Transitive Property of Equality

a+b=b+a Symmetric Property of Equality Reflexive Property of Equality Transitive Property of Equality Communitive Property for Addition

Communitive Property for Addition

If a=b, then a-c=b-c Vertical Angle Congruence Theorem Distributive Property Substitution Property of Equality Subtraction Property of Equality

Subtraction Property of Equality

If a=b, then ac=bc Transitive Property of Equality Multiplication Property of Equality Addition Property of Equality Distributive Property

Multiplication Property of Equality

a=a Reflexive Property of Equality (reflection) Right Angle Congruence Theorem Subtraction Property of Equality Multiplication Property of Equality

Reflexive Property of Equality (reflection)

If a=b, then b can be substituted for a in any expression Addition Property of Equality Substitution Property of Equality Transitive Property of Equality Multiplication Property of Equality

Substitution Property of Equality

If a=b and b=c, then a=c Transitive Property of Congruence Transitive Property of Equality Distributive Property Linear Pair Postulate

Transitive Property of Equality

If AB ≅ CD and CD ≅ EF, then AB ≅ EF. Addition Property of Equality Symmetric Property of Equality Multiplication Property of Equality Transitive Property of Congruence

Transitive Property of Congruence

What are the properties of a group? All of the above I. Set S is closed under the operation ⋆ II. The associative property applies to the system III. There is an identity element in set S IV. Every element has an inverse in set S None of the above Cannot be determined

I. Set S is closed under the operation ⋆ II. The associative property applies to the system III. There is an identity element in set S IV. Every element has an inverse in set S

If f(x) in Z[x] is primitive, then f(x) is reducible in Z[x] if and only if f(x) is reducible in Q[x]. Unique Factorization Domain (UFD) primitive polynomial Reducibility and Primitive Polynomials Isomorphism from F[x]/ to F(a)

Reducibility and Primitive Polynomials

An integral domain R where every nonzero nonunit element can be written as a unique product of irreducible elements. Ascending Chain Condition UFD and Primes f(x) Splits Unique Factorization Domain (UFD)

Unique Factorization Domain (UFD)

Abstract Algebra

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