Quote (feanur @ Nov 1 2015 08:07pm)
by "groups", you probably mean "sets", by "equivalent", you probably mean "equipotent" (same cardinality).
a) is true :
if A is finite, then " A ∩ B equipotent to A " implies A ∩ B is finite too, and since A ∩ B ⊆ A, that implies A ∩ B = A, then in turn, that A ∪ B = B.
b ) is false :
Let A = {0} and B={0;1}.
A ∩ B = A, A ∪ B ≠ A but B is finite.
c) is true :
if A is finite, then A ∩ B = A (see above), that implies A ⊆ B.
Thank you!!!