Symmetry in Operations Math Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
easyDoes \(8 - 5\) equal \(5 - 8\)? What does this tell us about subtraction's symmetry?
Solution
- 1 \(8 - 5 = 3\).
- 2 \(5 - 8 = -3\).
- 3 \(3 \neq -3\), so subtraction is NOT symmetric (not commutative).
Answer
No — subtraction lacks symmetry
Subtraction is not commutative: \(a - b \neq b - a\) in general. Order matters, so there is no symmetry.
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 2 mediumFor addition, show that if (a + b = c), then (b + a = c) (symmetry). Use (a=12, b=7).
Example 4 mediumIs (16 div 4 = 4 div 16)? What does this tell us about division's symmetry?