Math question pls help?

2008-01-28 3:45 am
Prove, without using Venn diagrams, that the statements
A ⊂ B
A ∩ B = A, and
A ∪ B= B,
are equivalent to each other for all sets of A and B

Please explain your answer.

回答 (3)

2008-01-28 4:00 am
✔ 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!! :-)
2008-01-28 3:55 am
A⋂B ≠ A   ⇒   ∃ x∊A such that x∉B   ⇒   A⊄B

A⋃B ≠ B   ⇒   ∃ x∊A such that x∉B   ⇒   A⊄B
2016-10-15 7:18 pm
The roots (or particularly the comparable numbers with opposite sign) would desire to function to the midsection coefficient of the quadratic. the midsection coefficient is seven, 2 numbers that upload to seven and selection by potential of one are 3 and four. considering the fact that 3+4 = 7 and four - 3 =a million q would be those comparable numbers accelerated at the same time. 3*4=12 So q = 12.


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