binary operations in relation and functions class xii

A is called the composite function of f and g. (ii) If f and g be functions from A to A then fog and gof are both defined. In general fog gof. A function from A x A into A is called a binary operation on A..

An expression consisting of combinations of binary operations +, . and unary operation and a finite number of elements of a Boolean algebra is called a Boolean function..

Note that the 'NOT' operation is a unary operator, whereas 'AND' and 'OR' operators are binary operators. We have already discussed what a Boolean function is. Here is a formal definition for Boolean expression and Boolean function..

Let (B, +, ., ', 0, 1) be a Boolean algebra where B is a non-empty set, '+' and '.' are binary operations, ' is a unary operation with two special elements 0 (Zero element) and 1 (unit element). Let x 1 , x 2 , x 3 .x n are in B. Then Boolean expression in x 1 , x 2 ..

Modems - The 'modem' is a contraction of the term modulator-demodulator. It is a conversion that facilitates the transmission and reception of the data over the public switched telephone network (PSTN). The data of interest may be digital signals generated by computers or service providers. In such..

Different forms of numbers Scientific notation, square roots, exponents, radicals, absolute value, factorial, logarithms Properties of numbers Estimation of solutions Sequences and series Proportionality/direct variation, exponential/fractional expressions Patterns, relations and ..

In 1886 the French chemist Francois Marie Raoult carried out a series of experiments to study the vapor pressure of a number of binary solutions containing non-volatile as well as volatile non electrolyte solutes. On the basis of the results of the experiment he stated a law known as Raou..