For all sets A, B and C, A x (B - C) = (A x B) - (Ax C). True or False? Prove it?

Set Theory Question (Cartesian Products):For all sets A, B and C, A x (B - C) = (A x B) - (Ax C). True or False? Prove it?
It is true.


Hint for proof: Compare components in i, j, k direction separately.


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To the answerer below me,


You are supposed to prove the conclusion that distributive property can be extended to cross product of vectors. But, you can not use the conclusion in your proof.For all sets A, B and C, A x (B - C) = (A x B) - (Ax C). True or False? Prove it?
Yes, you use the distributive property, which states that:


a(b+c) =ab+ac


Same thing with subtraction: a(b-c)=ab-ac


So if you think of ax as one number in this case, then:


ax(b-c)=axb-axc, so yes, it is true

short hair cuts