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4. BC 5. (A ∪ B)C 6. (A ∩ B)C 7. A - B 8. B - A A B Bc A B (A U B)c A B B - A A B ()A B c A B A - B ...

9. AΔB = (A-B) ∪^ (B-A) (A-B) ∪^ (B-A) De Morgan’s laws on complementation The complement of the union of any two sets is equal ...

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RELATIONS Relation A relation is a correspondence between the elements of two sets A and B. A relation is denoted by the letter ...

Symmetric relation A relation R, on a set A is said to be symmetric, if aRb and bRa, for all a, b ∈ A. In symbols, aRb implies ...

FUNCTIONS Function Let A and B be any two non-empty sets. Let f denote some rule which associates with every element of A, a un ...

f : A→B and f(x) = x^2 Here 1, 4, 7 and 8 are pre-images and 1, 16 49, 64 are images Verbal explanation assisted by two sets pre ...

Each and every element of the domain should have an image in the co-domain, but all the elements in the co-domain need not have ...

Eg. : f : A→B and f(x) = x^2 Into function The mapping f : A→B is called into, if there is at least one element of set B which ...

Constant function A function f : A→B is called a constant function if every element of A has the same image in B. In other word ...

Consider A = {1, 2, 3} B = {1, 8, 27} f(x) = x^3 In ordered pairs, f = { (1,1), (2,8), (3,27) } Arrow diagram A function can be ...

0 2 (^123456) 4 6 8 10 12 (1,1) (2,4) (3,9) Y X Braille lines may also be prepared to teach the concept of graph. A geo-board wi ...

BINARY SYSTEM Binary system The system which uses only two digits namely 0 and 1 is called the binary system. The system which ...

Conversion from denary to octal A denary number can be converted into an octal number by dividing the given number by 8 continu ...

Binary subtraction As in the case of binary addition, in binary subtraction also the following rules are to be followed. 0 – 0 ...

Multiplication table If the child is aware of these rules, then the process of multiplication involves only addition which the c ...

MATRICES Matrix A matrix is an arrangement of numbers in rows and columns. In a matrix the numbers arranged horizontally consti ...

If A is a matrix of order m × n, then, A = ⎟⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ m 1 m 2 m 3 mn 31 32 33 3 n 21 22 23 2 n 11 12 13 1 n a ...

Square Matrix A matrix with equal number of rows and columns is said to be a square matrix. Eg. : B = ⎟⎟ ⎠ ⎞ ⎜⎜⎝ ⎛ − − 3 6 2 4 ...

Row Matrix A matrix with a single row is said to be a row matrix. Eg : B = () 1 − 2 − 3 The matrix B has only one row and thre ...