Algebra Chapter 2.07 Proofs Flashcards

Questions and Answers

What does the reflexive property of equality state?

For all real numbers a, a = a (correct)

For all real numbers a and b, if a = b, then b = a

For all real numbers a, b, and c, if a = b and b = c, then a = c

For all real numbers a, b, and c, if a = b then a + c = b + c

What does the symmetric property of equality state?

For all real numbers a and b, if a = b, then b = a (correct)

For all real numbers a, a = a

For all real numbers a, b, and c, if a = b then a + c = b + c

For all real numbers a, b, and c, if a = b and b = c, then a = c

What does the transitive property of equality state?

For all real numbers a, b, and c, if a = b then a + c = b + c

For all real numbers a and b, if a = b, then b = a

For all real numbers a, b, and c, if a = b and b = c, then a = c (correct)

For all real numbers a, a = a

What does the addition property of equality state?

For all real numbers a, b, and c, if a = b then a + c = b + c Signup and view all the answers

What does the subtraction property of equality state?

For all real numbers a, b, and c, if a = b, then a - c = b - c Signup and view all the answers

What does the multiplication property of equality state?

For all real numbers a, b, and c, if a = b, then ac = bc Signup and view all the answers

What does the division property of equality state?

For all real numbers a, b, and c, if a = b and c ≠ 0, then a/c = b/c Signup and view all the answers

Study Notes

Properties of Equality

Reflexive Property of Equality: Any real number is equal to itself, expressed as ( a = a ).
Symmetric Property of Equality: If one real number equals another, the reverse is also true; if ( a = b ), then ( b = a ).
Transitive Property of Equality: A chain of equalities leads to a conclusion of equality; if ( a = b ) and ( b = c ), then ( a = c ).

Addition and Subtraction Properties

Addition Property of Equality: If two numbers are equal, adding the same number to both sides maintains the equality; if ( a = b ), then ( a + c = b + c ).
Subtraction Property of Equality: Similar to addition, subtracting the same number from both sides of an equation preserves equality; if ( a = b ), then ( a - c = b - c ).

Multiplication and Division Properties

Multiplication Property of Equality: Multiplying both sides of an equality by the same non-zero number keeps the equality intact; if ( a = b ), then ( ac = bc ).
Division Property of Equality: Dividing both sides of an equality by the same non-zero number maintains equality; if ( a = b ) and ( c \neq 0 ), then ( \frac{a}{c} = \frac{b}{c} ).

Description

Test your knowledge on the properties of equality with these flashcards. Each card covers a fundamental property such as reflexive, symmetric, transitive, and addition. Perfect for reinforcing your understanding of algebraic proofs.