What’s covered / Class 11 Mathematics / Ch 1 1. Sets 11 topics 2 h
Chapter 1 of NCERT Mathematics for Class 11: Sets . Three sections — What a set is, and how one gets written down, Sets sitting inside other sets and Building new sets from old. 11 videos, 2 h in all.
Worked answers to the 49 exercise questions in this chapter: Exercise 1.1 · Exercise 1.2 · Exercise 1.3 · Exercise 1.4 · Exercise 1.5 · Miscellaneous Exercise
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Part 1
What a set is, and how one gets written down 12 min Why "well-defined" is the whole difference between a set and a heap Name the five greatest musicians who ever lived, then name the odd numbers below ten. Both are collections and both are one sentence long, but only one of them survives being handed to a second person. That difference - not size, not whether the members are numbers, not whether you can write them all down - is the entire entry requirement for a set. 12 min · 13 parts 14 min Listing the members versus stating the property they share A set can be written two ways: list the members, or state the property they share. They look like equal partners and they are not. The explanation shows exactly where listing runs out, and why the property is the primary thing with the roster only a report of it. 14 min · 14 parts 13 min A set with nothing in it, and sets you cannot finish listing Two collections of students. One has a number nobody has ever counted. The other has no members at all - and not because the school is small. Telling those two apart without ever seeing a list is what 'empty' and 'infinite' actually mean, and both verdicts are reached the same way: by arguing with the condition. 13 min · 14 parts 14 min Why order and repetition cannot make two sets different One, two, three, four. And three, one, four, two. Same set, or different? Almost everyone answers instantly and then struggles to say why - so the explanation asks the harder question first: what could possibly make two sets different at all? 14 min · 14 parts Part 2
Sets sitting inside other sets Part 3
Building new sets from old 12 min Turning a claim about sets into a picture you can read off Two overlapping circles get drawn in every course on sets, and almost everyone treats them as a sketch beside the real work. Drawn one particular way they ARE the real work - and drawn the way most people draw them, they will happily agree with things that are false. 12 min · 16 parts 15 min Union and intersection, and what it means for two sets to miss each other entirely Union and intersection are usually taught as two new things a set can do. They are not new and they are not two things: they are the words 'or' and 'and' pointed at a pair of sets, and once you see that, the ten laws you were told to memorise turn into two four-row tables you can rebuild from scratch in your head. 15 min · 16 parts 14 min Difference and complement: the same idea with and without a universal set Remove {2, 4, 6, 8} from {1, 2, 3, 4, 5, 6} and three numbers survive; the other way round, only one does. Difference is the one set operation that minds the order. 14 min · 14 parts 14 min Why complementing turns each of the two operations into the other Outside {2, 3} and outside {3, 4, 5}, together, name exactly {1, 6} — same as the complement of their union. Complementing each set apart, the tempting shortcut, misses by three. 14 min · 14 parts What you will be able to do State the condition a collection must satisfy before it may be called a set, and apply it as a decision procedure rather than reciting it Write a given set in roster form, using braces and commas, with no member repeated Decide, from a defining condition alone, whether the set it describes has any members at all State the condition under which two sets are equal, as a check running in both directions State the containment condition as an implication about an arbitrary member State the printed containment relations among the number systems, including the one that is a non-containment State what role the universal set plays and why it is chosen rather than derived Name what the rectangle and each closed curve stand for in a Venn diagram Form the union and the intersection of two given sets, in roster form Form the difference of two sets in either order and show that the two results differ State both of De Morgan's laws for two subsets of a stated universe What this chapter assumes you already know Natural numbers, integers, rational and real numbers as separate number systems Prime numbers, and factorising a whole number into primes Solving a quadratic by factorising, e.g. finding both roots of a quadratic whose factors are visible Reading a two-letter Greek symbol and a struck-through symbol as opposites The everyday word collection — a card pack, a crowd, a sports team The belongs-to symbol and its negation Divisors and prime factorisation of a two- or three-digit number Solving a quadratic by factorising, including one with a negative root Where people usually slip up Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.
"A set has to be a collection of numbers." "Well-defined means you can write the members down." "If it is infinite it is not well-defined." "A ranking is fine as long as experts agree." "15 is a prime factor of 30 because it divides 30." "The questions in this chapter is too odd to be a set." "Once a collection is refused, we can still talk about it loosely." "Writing an element twice makes the set bigger." 
