Question

In a survey conducted for students studying in class 10 of Shree Sharada Secondary School, which of Pokhara, Lumbini and Ilam would be suitable for an educational trip, 40 people said that Pokhara, 30 people would go to Lumbini and 45 people would go to Ilam. While 15 students of that class said that all three places are suitable, 5 students did not express any opinion.

(a) Let P, L and I denote the number of students for whom Pokhara, Lumbini and Ilam respectively are suitable, and write the group of students for whom all places are suitable in numerability notation.

Answer 1

The group of students who find all three places suitable for the educational trip, Pokhara, Lumbini, and Ilam, can be represented in set theory as the intersection of sets P, L, and I, which is denoted as P ∩ L ∩ I = 15. Students not expressing any opinions are outside these sets.

Step-by-step explanation:

In the context of the educational trip survey for class 10 students at Shree Sharada Secondary School, we will represent students' preferences for different destinations using set notation. To express the group of students who find all three places — Pokhara, Lumbini, and Ilam — suitable, we can denote this as the intersection of three sets P, L, and I.

The number of students who find Pokhara suitable is denoted by P, Lumbini by L, and Ilam by I. Among them, 15 students found all three places suitable. In set theory, the intersection of three sets is denoted by P ∩ L ∩ I. Therefore, the group of students who find all three places suitable can be represented as P ∩ L ∩ I = 15. Remember, the symbols used here (∩) denote the intersection, where an element is a member of all the sets involved. On the other hand, 5 students did not express any opinion. They would not be included in any of the set preferences P, L, or I since they are essentially outside of these sets, often referred to as being in the set's complement or outside the universal set being considered for the survey.