Mathematics For 12th Class students

Addition theorem on Inverse Trigonometric Function. In this video I  proved the following three theorems. These theorems frequently asked in Boards exam. I have given you a step by step the proof of each theorem one by one. Don’t by heart the theorems understand the logic and practice them by writing.

In this post we are going to see two types of examples on the application of logic to the switching circuits.   A) how to express the given circuit in symbolic form of logic and B) how to construct the switching circuits if the logical statements are given.   So let’s begin. Ex. A) Express the following circuits in symbolic form of logic. In the circuit there are one S1 switch, two S2’ switches, one S3 switch and one S3’ switch. Let p: the switch S1 is closed.             ~q: the switch S2’ is closed.              r: the switch S3 is closed.          \  ~r: the switch S3’ is closed. The switch S2’ and S3 are connected in parallel and they are connected in series with the switch S1. Its symbolic form is p & (~q v r) . The switches S2’ and S3’ are connected in series. Its symbolic form  is...

We know that a statement in logic is either true or false.  The same situation occurs in electric switches.  A working switch is either on (closed) or off (open). If a switch is ‘on’ it allowed electric current to pass the circuit and lamp glows and if the switch is ‘open’ it does not allow current to pass the circuit and lamp does not glow. We shall denote ‘on’ switches by letters S, , , ,… and open switches are denoted by letters S’, , ,…But the symbol is used to denote both the switches are the same   only differ by the letters S and S’. Let the statement p denote the ‘switch S is closed’ and lamp with light by l. Then its symbolic form is p   l. Let ~p: the switch S’ is closed and lamp with no light by l’ Then its symbolic form is ~p   l’. Switches connected in the circuit in two different ways 1. In series 2. In parallel. 1. Switches connected in series Add ca...