Question

Let A, B, and C be sets where AnBnc =0. Is it true that |AU BUC| = |A| + |B| + |C|? (Compute examples before trying to prove this.) some

Answer 1

Answer: Hello!

So we have the sets A, B and C, and we also know that A∩B∩C = 0, (this means that there is not a common element to all the sets) and we want to know if it implies that A∪B∪C = IAI + IBI + ICI

Let's find a counterexample!

Let's suppose that A and B have an object in common, but this object is not in C, then we still have that A∩B∩C = 0 but not A∪B∪C = IAI + IBI + ICI.

suppose that A = {1, 2}, B = {2,3}, C={4.5}

then  A∩B∩C = (A∩B)∩C = {2}∩{4,5} = 0

And because A and B have an element in common, the second part is not true.