Here are the step-by-step solutions for the problems in Exercise 1 (a).
1. Difference between a collection and a set
โ Collection: Any group of objects.
โ Set: A well-defined collection of distinct objects.
โ Reason: For a collection to be a set, there must be no ambiguity about whether an
object belongs to it. For example, "the collection of tall people" is not a set (it's
subjective), but "the collection of people over 6 feet tall" is a set.
2. Which collections are sets?
โ (i) The collection of intelligent students in India: Not a set. "Intelligent" is subjective
and not well-defined.
โ (ii) The collection of positive multiples of 5: Is a set. It is well-defined: $\{5, 10, 15,
\dots\}$.
3. Vowels in the English alphabet which precede $s$
The vowels are $\{a, e, i, o, u\}$. All of these come before '$s$' in the alphabet.Answer: $\{a, e,
i, o, u\}$
4. List all elements (Roster Form)
โ (i) : $A = \{1, 3, 5, 7, \dots\}$
โ (ii) : $B = \{0, 1, 2, 3, 4\}$
โ (iii) : $C = \{-2, -1, 0, 1, 2\}$
โ (iv) : $D = \{L, O, Y, A\}$
โ (v) : $E = \{\text{February, April, June, September, November}\}$
โ (vi) : $F = \{b, c, d, f, g, h, j\}$
5. Solution set of $x^2 + x - 2 = 0$
Factorizing: $(x + 2)(x - 1) = 0 \Rightarrow x = -2, 1$.Answer: $\{-2, 1\}$
6. Write in Roster Form
โ (i) Vowels before : $\{a, e\}$
โ (ii) Prime numbers between 6 and 30: $\{7, 11, 13, 17, 19, 23, 29\}$
โ (iii) : $3x < 26 \Rightarrow x < 8.66$. Natural numbers are $\{1, 2, 3, 4, 5, 6, 7, 8\}$.
โ (iv) : $(x+2)(x+3)=0 \Rightarrow \{-2, -3\}$
7. Enumerate the elements
โ (a) : Roots are $1, 2$. Answer: $\{1, 2\}$
