Algebraic proofs - Logic

Algebraic proofs


Let a,b,a,b, and cc be real numbers. Then here are some of the properties of equality:
Reflexive Property: For every number aa, then a=aa=a.
Symmetric Property: For all numbers aa and bb , if a=ba=b , then b=ab=a .
Transitive Property: If a=ba=b and b=cb=c , then a=ca=c .
Substitution Property: If a=ba=b , then bb can be substituted for aa in any equation.
Addition Property: If a=ba=b , then a+c=b+ca+c=b+c .
Subtraction Property: If a=ba=b , then a?c=b?ca?c=b?c .
Multiplication Property: If a=ba=b , then ac=bca\cdot c=b\cdot c .
Division Property: If a=ba=b , then ac=bc\frac{a}{c}=\frac{b}{c} .
Distribution Property: a(b+c)=ab+aca(b+c)=ab+ac

When you solve an equation, you will want to use to the two-column proof. For example, if you want to show that x=1x=1 for the equation 2(x+1)+1=52(x+1)+1=5 , then it will look like this:
Statements Reasons
2(x+1)+1=52(x+1)+1=5 Given
2x+2+1=52x + 2 + 1 =5 Distributive Property
2x=22x=2 Subtraction Property
x=1x=1 Division Property
  • Intro Lesson
    Algebraic Proofs Overview:
  • 1.
    Understanding the Properties of Equality
    State which property was used in each statement:
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Algebraic proofs

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