A group of 62 students were surveyed, and it was found that each of the students surveyed
like at least one of the following three fruits:
apples, bananas, and guavas.
34 liked apples, 30 liked bananas, 33 liked
guavas, 11 like apples and bananas, 15 liked
bananas and guavas, 17 like apples and
guavas, 5 liked three fruits. (20 pts)
• How many students liked apples, but not
bananas and guavas?
. How many students liked bananas only?
• How many students liked apples or bananas
but not guavas?
• How many students liked bananas or guavas
or apples?
• How many students liked like apples and
guavas but not bananas?

students liked apples, but not bananas and guavas at the same time. ( students liked apples and liked neither bananas nor guavas.)

students liked bananas only.

students liked apples or bananas but not guavas.

students liked bananas or guavas or apples, (That is the number of students that liked one or more of the three fruits.)

students liked apples and guavas but not bananas.

Step-by-step explanation:

Start by drawing a Venn Diagram. (Refer to the first attachment.)

Using information from the question, fill in the number of students in each section.

Start with intersection of all three circles denotes the set of surveyed students that liked all three fruits.

The question states that there are students in this set. Besides, this set isn't a superset of any other set. Therefore, write the number in the corresponding place without doing any calculation.

Continue with the intersection of students that liked two fruits only. For example, the question states that surveyed students liked apple and bananas. However, that students also include the surveyed students that liked all three fruits (apple, banana, and guava.) Therefore, only surveyed students liked apple and banana only (but not guava.)

Similarly:

The question states that surveyed students liked guavas. However, among that students:

Therefore, only surveyed students liked guava but neither apple nor banana (guava only.)

Similarly:

Among the surveyed students, of them liked none of the three fruits.

Refer to the second diagram attached for the Venn Diagram with the corresponding numbers.

Students that liked apples but not bananas and guavas at the same time include:

These three subsets include surveyed students.

It was previously found that students liked bananas only.

Students that liked apples or bananas but not guavas include:

That include surveyed students.

Among these surveyed students, of them liked at least one of the three fruits.

It was previously found that among these surveyed students, of them liked apples and guavas only. That gives the number of students that liked apples and guavas, but not bananas.

step-by-step explanation:

b and c