Post-Reading Activity.

Ex. 7. Answer the following questions:

1. What is a set? 2. What are the elements of the set? 3. What sets are of interest in mathematics? 4. What do we use to represent sets and elements? 5. What set is considered to be known? 6. What is the simplest way of specifying a set? 7. What is the standard notation for a set? 8. What sets are equal? 9. How can we specify the elements of a set? 10. How many members may a set have? 11. What is an empty set? 12. How is an empty set represented? 13. Does an empty set exist at all?

Ex. 8. Match the English words and word combinations with the Russian equivalents.

exact property; to enclose the list in curly brackets; to keep rigidly to the convention; set theory; just one element; a finite set of elements; elements listed; concrete sets; a way of specifying a set; the same elements; infinitely many elements; standard notation; abstract objects; a complete list; it makes no difference; the sets of interest in mathematics; members of the set.

члены множества; множества, вызывающие интерес в математике; конкретные множества; абстрактные объекты; способ определять множество; обычно принятое обозначение; заключить перечень в фигурные скобки; одни и те же элементы; перечисленные элементы; точное свойство; бесконечное число элементов; полный перечень; конечное число элементов; только один элемент; не имеет значения; теория множества; строго придерживаться условия.

Ex. 9. Fill in the blanks with the words from the box.

empty, members, to list, notation, specifying, difference, precisely, the same

1. The objects belonging to the set are the elements or … of the set. 2. There are many ways of … a set. 3. The simplest way of specifying a set is … all the members. 4. The standard … is to enclose the list in curly brackets. 5. Two sets are equal if they have … elements. 6. The order inside the brackets makes no … 7. Instead of a list, we give a property which specifies … the elements. 8. A set with no elements is called an … set.

Ex. 10. Ask questions for which the given sentences are answers.

1. A set is a collection of objects. (What?) 2. The objects belonging to the set are the elements or members of the set. (Which?) 3. The sets of interest in mathematics always have members which are abstract mathematical objects. (What?) 4. In the algebra of sets we use letters to represent sets and elements. (Where?) 5. A set is considered to be known if we know what its elements are. (When?) 6. There are many ways of specifying a set. (How many?) 7. The standard notation is to enclose the list in curly brackets. (What?) 8. Two sets are equal if they have the same elements. (When?) 9. Instead of a list, we give a property which specifies precisely the elements of the set. (What?) 10. For sets with infinitely many members, it is impossible to give a complete list. (Which?) 11. The mathematical notion of a set allows sets with only one member or even no members at all. (What?) 12. A set with no elements is called an empty set. (What?) 13. All empty sets are equal. (What?)

Ex. 11. Find out whether the statements are true or false. Use introductory phrases.

Exactly. Quite so. Quite the contrary.