1. Sets and their Representations

2. The Empty Set, Finite and Infinite Sets, Equal Sets

3. Subsets, Power Set, Universal Set

4. Venn Diagrams, Operations on Sets

5. Complement of a Set

6. Union and Intersection of Two Sets

Set: A set is a well-defined collection of objects.

Representaiton of sets:

(i) Roster or Tabular form, (ii) Rule method or set builder form.

Surds:

(i) The surd conjugate of √a + √b (or a + √b) is √a - √b (or a - √b) and conversely. 

(ii) If a is rational, √b is a surd and a + √b (or, a - √b) = 0 then a = 0 and b = 0. 

(iii) If a and x are rational, √b and √y are surds and a + √b = x + √y then a = x and b = y.

Laws of Indices:

(i) aᵐ ∙ aⁿ = aᵐ + ⁿ 

(ii) aᵐ/aⁿ = aᵐ - ⁿ 

(iii) (aᵐ)ⁿ = aᵐⁿ 

(iv) a = 1 (a ≠ 0). 

(v) a-ⁿ = 1/aⁿ 

(vi) ⁿ√aᵐ = aᵐ/ⁿ 

(vii) (ab)ᵐ = aᵐ ∙ bⁿ. 

(viii) (a/b)ᵐ = aᵐ/bⁿ 

(ix) If aᵐ = bᵐ (m ≠ 0), then a = b. 

(x) If aᵐ = aⁿ then m = n.