State whether or not the following elements form a set; if not, give reason:
(i) All the easy problems in your text book.
(ii) All the three-sided figures.
(iii) The first five whole numbers.
(iv) All the tall boys of your class.
(v) The last three days of a week.
(vi) All the triangles that are difficult to draw.
(vii) The first three letters of the English alphabet.
(viii) All the tasty fruits.
(ix) All the clever boys of class 6.
(x) All the good schools in Delhi.
(xi) All the girls in your class whose heights are less than your height.
(xii) All the boys in your class whose heights are more than your height.
(xiii) All the problems in your Mathematics book that are difficult for Amit.
Answer
A set is a collection of well-defined objects.
(i) It is not a set; some problems may be easy for one person but may not be easy to some other person. So, the objects are not well defined.
(ii) It is a set; the three-sided figures (triangles) are well defined.
(iii) It is a set; the first five whole numbers, i.e. 0, 1, 2, 3 and 4, are well defined.
(iv) It is not a set; it is not mentioned that the boys must be taller than which boy. If we consider three boys A, B and C, boy A can be taller than B but not necessarily taller than C. So, the objects are not well defined.
(v) It is a set; the last three days of a week, i.e. Friday, Saturday and Sunday, are well defined.
(vi) It is not a set; it may be difficult for one student to draw a given triangle, but to some other student it may not be difficult to draw the same triangle. So, the objects are not well defined.
(vii) It is a set; the first three letters of the English alphabet, i.e. A, B and C, are well defined.
(viii) It is not a set; a fruit may be tasty for one person and may not be tasty to other person/persons. So, the objects are not well defined.
(ix) It is not a set; clever in what respect? The word 'clever' is not well defined.
(x) It is not a set; all the people cannot find the same schools as good schools. So, the objects are not well defined.
(xi) It is a set; the heights are compared with a fixed height (your height), so it can be clearly decided which girls are to be included. The objects are well defined.
(xii) It is a set; the heights are compared with a fixed height (your height), so it can be clearly decided which boys are to be included. The objects are well defined.
(xiii) It is a set; it can be clearly found which problems are difficult for Amit and which are not. So, the objects are well defined.