Question

If A ⊂ B, then A ∩ B = A ∪ B.



always

sometimes

never

Answer 1

For example
A = {2, 4, 6}
B = {1, 2, 3, 4, 5, 6}

A ∩ B = {2, 4, 6}
A ∪ B = {1, 2, 3, 4, 5, 6}

Answer 2

In this case, A ⊂ B, but \( A ∩ B \ne A ∪ B\)

Answer 3

What you have to do is look for more cases that might support the original assumption.

Answer 4

Using Venn Diagrams may help with the process.

Answer 5

Depends whether you allow set A or B to be equal.
If A = B, then A is subset of B, then

A union B = A intersect B

So, sometimes it's true

Answer 6

okay thank you

Answer 7

As far as I know, there is no difference between ⊆ and ⊂. However, depends on your instructor, ⊆ could mean the usual subset, while ⊂ is the proper set.

If ⊂ means proper set, then statement above is always false