✔ 最佳答案
Hi,
Sorry but the statements
A ⊂ B
A ∩ B = A, and
A ∪ B= B,
are NOT equivalent to each other for all sets of A and B
If A = {3,4,5} and B = {5,7}, then:
A ⊂ B is not true because set A is not a subset of set B.
A ∩ B, the intersection of what sets A and B have in common, is clearly NOT set A.
A ∪ B, the union of sets A and B, is NOT set B.
However, if you knew that A ⊂ B was true, then A ∩ B = A, and A ∪ B= B would both be true. For example if A = {6,7,8} and B = {6,7,8,9,10}, then clearly A ⊂ B is true because 6, 7, and 8 are included in both sets.
A ∩ B, the intersection of what sets A and B have in common, is set A because A includes 6,7, and 8 while B includes 6,7,8,9, and 10.
A ∪ B, the union of sets A and B, is set B because all of 6,7,8 and 6,7,8,9, and 10 would be 6,7,8,9, and 10, set B.
I hope that helps!! :-)