Q5 of 162 Page 1

For any two sets A and B, show that the following statements are equivalent:

A ∩ B = A.

Finally, now we need to show 4 ⇒ 1.


So, assume A ∩ B = A.


To show: A ⊂ B


∵A ∩ B = A, therefore A⊂B, and so (4) ⇒ (1) is true.


More from this chapter

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5

For any two sets A and B, show that the following statements are equivalent:

A – B = ϕ

 5

For any two sets A and B, show that the following statements are equivalent:

A ∪ B = B

 6

For three sets A, B, and C, show that

A ∩ B = A ∩ C need not imply B = C.

 6

For three sets A, B, and C, show that

A ⊂ B C – B ⊂ C – A