I. Cartesian product 1. A B (x, y) / x A and y B (a, b) (c,d) (a, b)
(c,d) a c and b d If A B then either one of A or B is null set
2. If n (A) = m and n (B) = n then n(A×B) = mn 3. If 2 n(A B) m then n (A
B) (B A) m 4. A B B A(in general)but A B B A A B
where A and B 5. A (B C) (A B) (A C) and A
(B C) (A B) (A C) and A (B C) (A B) (A C) 6.
(A B) (C D) (A C) (B D)
RELATION 1. A relation from A to B is a subset of A ×B, If (x, y) R means x
related to y. ie., if xRy then (x, y) R . ie R = (x, y) / x A, y B If n(A)
= m and n(B) = n then number relations from A to B = 2mn 2. Inverse relation
If 1 R :A B then R : B A 1 R (y, x) /(x, y) R Note : Dom
(R) = Ran (R-1) and Ran (R) = Dom(R-1) 3. Relation on a set R :A A is the
relation on a set A No. of relation on a set have n elements = 2 n 2
Part II - Functions
1) Graphs of functions a) Basic graph (functions) b) Simple transformation &
graphs
2) Domain & Range
3) Types of functions a) one-one function b) many - one c) Onto d) Into e)
Bijective function N.B Number of above functions should be explained
4) Composite functions a) fog and gof (explanation) b) Properties of
composite function
5) Invertable functions a) Inverse of an element b) Inverse of a function c)
Properties of inverse with geometrical explanation
6) Even & Odd functions a) Analytical & Graphical approaches b) Properties
7) Periodic functions a) Algebraic functions and their fundamental periods b)
Trigonometric function and its fundamental periods c) Properties of periodic
function
(c,d) a c and b d If A B then either one of A or B is null set
2. If n (A) = m and n (B) = n then n(A×B) = mn 3. If 2 n(A B) m then n (A
B) (B A) m 4. A B B A(in general)but A B B A A B
where A and B 5. A (B C) (A B) (A C) and A
(B C) (A B) (A C) and A (B C) (A B) (A C) 6.
(A B) (C D) (A C) (B D)
RELATION 1. A relation from A to B is a subset of A ×B, If (x, y) R means x
related to y. ie., if xRy then (x, y) R . ie R = (x, y) / x A, y B If n(A)
= m and n(B) = n then number relations from A to B = 2mn 2. Inverse relation
If 1 R :A B then R : B A 1 R (y, x) /(x, y) R Note : Dom
(R) = Ran (R-1) and Ran (R) = Dom(R-1) 3. Relation on a set R :A A is the
relation on a set A No. of relation on a set have n elements = 2 n 2
Part II - Functions
1) Graphs of functions a) Basic graph (functions) b) Simple transformation &
graphs
2) Domain & Range
3) Types of functions a) one-one function b) many - one c) Onto d) Into e)
Bijective function N.B Number of above functions should be explained
4) Composite functions a) fog and gof (explanation) b) Properties of
composite function
5) Invertable functions a) Inverse of an element b) Inverse of a function c)
Properties of inverse with geometrical explanation
6) Even & Odd functions a) Analytical & Graphical approaches b) Properties
7) Periodic functions a) Algebraic functions and their fundamental periods b)
Trigonometric function and its fundamental periods c) Properties of periodic
function
