Proofs...Mr Legutco
For Midterms we have to know proofs... so heres a list
Terms
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- Associative Property for Addition
- (a+b)+c=a+(b+c)
- Subtraction Property of Equality
- a-c = b-c
- Identity Property for Multiplication
- There exists an element 1 € R, such that for each a € R: a•1=a & 1•a=a
- Division Rule
- For all real numbers a and all nonzero real numbers b , a-b=a+(-b)
- Addition Property of Equality
- a+c = b+c; c+a = c+b
- Inverse Property of Addition
- a + (-a)=0
- Multiplication Property of Zero
- For all real numbers a, a•0=0 and 0•a=0
- Reflexive Property of Equality
- a=a
- Identity Property for Addition
- There exists an element -a E R, for each a E R, such that: a+0=a & 0+a=a
- Transitive Property of Equality
- if a=b and b=c, then a=c
- Commutative Property for Addition
- a+b=b+a
- Property of the Opposite of a Sum
- For all real numbers a and b, -(a+b)=(-a)+(-b) That is, the opposite of a sum of real numbers is the sum of the opposites of the numbers.
- Symmetric Property of Equality
- if a=b then b=a
- Multiplication Property of -1
- For all real numbers a, a•(-1)=-a and (-1)•a=-a
- Subtraction Rule
- For all real numbers a and b, a-b=a+(-b)
- Closure Property for Multiplication
- ab is a unique real number
- Distributive Property for Mult. over Add.
- a(b+c)=ab+ac & (b+c)a=ba+ca
- Inverse Property of Multiplication
- There exists an element 1 ⁄a € R, for each nonzero a € R such that: 1/a•a=a & a•1/a=1
- Multiplication Property of Equality
- ac=bc; ca=cb
- Substitution Principle
- Since a+b and ab are unique, changing the numeral by which a number is named in an expression involving sums or products does not change the value of the expression. *This principle is used as a last resort for any basic math that does not involve either Identity Properties, either Inverse Properties, Multiplication Properties of Zero or -1
- Commutative Property for Multiplication
- ab=ba
- Division Property of Equality
- a/c = b/c (provided c ≠ 0)
- Closure Property for Addition
- a + b is a unique real number
- Associative Property for Multiplication
- (ab)c=a(bc)
- Properties of Opposites in Products
- For all real numbers a and b, (-a)b=-ab, a(-b)=-ab, (-a)(-b)=ab