Question

Given P = {apples, oranges, bananas, pears} and Q = {oranges, pears, grapes}, what is P ∩ Q?

a) P ∩ Q = 0 (empty set)
b) P ∩ Q = {oranges, pears}
c) P ∩ Q = {apples, oranges}
d) All of the above

Answer 1

Answer: Choice B

P ∩ Q = {oranges, pears}

Step-by-step explanation:

The notation P ∩ Q means "P intersect Q". It's the overlapped region of the Venn diagram. Both "oranges" and "pears" are in both sets at the same time. That's why they make up the final answer shown above.

Apples are found in set P, but not in set Q, so we cross "apples" off the list. Grapes aren't found in P, so we cross that off the list as well.

If there weren't any common shared fruits between the sets, then the answer would be "empty set". As the name implies, the empty set is the set with nothing inside it. Not even zero is an element of the empty set.

Answer 2

The intersection of sets P and Q, denoted P ∩ Q, includes the common elements 'oranges' and 'pears', thus the correct answer is P ∩ Q = {oranges, pears}.

Step-by-step explanation:

The question asks us to find the intersection of two sets P and Q, where P = {apples, oranges, bananas, pears} and Q = {oranges, pears, grapes}. The intersection of two sets, denoted by P ∩ Q, includes all the elements that are common to both sets. In this case, the elements oranges and pears are present in both set P and set Q. Therefore, the intersection of P and Q is P ∩ Q = {oranges, pears}.