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Is there any branch of mathematics in which it is false that If A = B, then B = A ? ?

Can the logical inference

If A = B, then B = A 

ever be false? Is there an algebra or type of logic or math entity in which this can be false? 

4 Answers

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  • 5 months ago
    Favorite Answer

    The relation "is equal to" is the canonical example of a binary equivalence relation which is reflexive, symmetric and transitive.

    If the equal sign (=) is being used to represent the "is equal to" relation, then it is always true that:

    A = A (reflexive)

    A = B → B = A (symmetric)

    A = B, B = C → A = C (transitive)

    But it is possible to redefine the meaning of the equal sign to where this wouldn't be true. So how are you defining '='?

  • Anonymous
    5 months ago

    Statement A = all dogs are 4 legged creatures.

    Statement B = All 4 legged creatures are dogs.

    B is not equal to A but A = B.

    Logic could be such branch.

    But if A and B are numbers, then it can't be false. 

  • fcas80
    Lv 7
    5 months ago

    All boy children are male.

    All males are not boy children.

  • 5 months ago

    I do not know everything ... anything is possible...

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