Answer:
O U ⊆ A ∪ B True
O U ⊆ A ∩ B False
O A ∪ B ⊆ U True
O B ⊆ U True
O A ⊆ U True
O A ∩ B ⊆ U True
Step-by-step explanation:
To prove the first part
Remember that any set is a subset of the universal set. Therefore it is true that
Now, given any it is true that
Now according to the information given initially
And then you know that
Therefore and using double inclusion
.
Now using the information just exposed
O U ⊆ A ∪ B True
O U ⊆ A ∩ B False
O A ∪ B ⊆ U True
O B ⊆ U True
O A ⊆ U True
O A ∩ B ⊆ U True