Question

Given U = {cat, dog, fish, goat, horse, llama, sloth}, A = {cat, dog, fish}, and B = {cat, fish, horse, sloth}. If (A ∩ B)' = {dog, goat, horse, llama, sloth}, determine A' ∪ B'.

{dog, goat, horse, llama, sloth}
{goat, horse, llama, sloth}
{dog, goat, llama}
{cat, fish}

Answer 1

We can start by finding (A ∩ B) using the given sets A and B.

A ∩ B = {cat, fish}

Next, we can find (A ∩ B)' by taking the complement of (A ∩ B) with respect to U.

(A ∩ B)' = {dog, goat, horse, llama, sloth}

Now, we can use De Morgan's law to find A' ∪ B'.

A' ∪ B' = (A') ∩ (B')'

To find A', we need to take the complement of A with respect to U.

A' = {goat, horse, llama, sloth}

To find B', we need to take the complement of B with respect to U.

B' = {dog, goat, llama}

Finally, we can take the intersection of (A') and (B')' to get A' ∪ B'.

(A') ∩ (B')' = {dog, goat, horse, llama, sloth} ∩ {cat, fish}

A' ∪ B' =

Answer 2

what do you get

Answer 3

{dog, goat, horse, llama, sloth} ?