Symmetry in Operations Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
For addition, show that if \(a + b = c\), then \(b + a = c\) (symmetry). Use \(a=12, b=7\).

Solution

  1. 1
    Compute \(12 + 7 = 19\).
  2. 2
    By symmetry, \(7 + 12 = 19\).
  3. 3
    Both equal 19, confirming the symmetric (commutative) property.
  4. 4
    Statement: \(a + b = c \Rightarrow b + a = c\).

Answer

19 in both cases
Symmetry in an operation means swapping the operands yields the same result. This is exactly the commutative property.

About Symmetry in Operations

When exchanging or swapping operands or roles in an operation produces the same result or a symmetrically related one.

Learn more about Symmetry in Operations →

More Symmetry in Operations Examples

Example 1 easy

Show that (5 + 3 = 3 + 5) and (5 times 3 = 3 times 5). What symmetric property do both share?

Example 3 easy

Does (8 - 5) equal (5 - 8)? What does this tell us about subtraction's symmetry?

Example 4 medium

Is (16 div 4 = 4 div 16)? What does this tell us about division's symmetry?

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