 in which we will see the different three notations, polished notation that is infix notation, prefix notation, and postfix notation. The learning outcome, student can comprehend polished notations, student will be able to recognize different types of polished notations. The content of the today's topics are statement, notations, type of polished notations, infix, prefix, and postfix. The definition, all the declarative sentences to which possible to assign one or only one, two possible truth values, either true or false. For example, India is a country, Delhi is capital of Maharashtra, this statement is false. These are the three statements we have considered. Out of that, the first statement, India's country has got the true value. Second, Delhi is the capital of Maharashtra, which has got the false value. Whereas the third one, we cannot assign either true or false value. So, according to our definition, it cannot be a statement. Notations, notations, rather how to symbolize all these simple statements. For example, consider, Ram went to school. This can be symbolized with any alphabet, say R. You can take A to Z, out of that, I have taken R. The second statement, consider, Sham went to the playground. Now, in this Sham went to the playground, you can consider, say yes. Now, if I combine these two statements, like Ram went to the school, and Sham went to the playground, this is called as a compound statement. And the simple statements are like, Ram went to the school is a simple statement. Sham went to the playground is a simple statement. When you combine these two simple statements, that becomes a compound statement, and it can be written as Ram went to the school, and Sham went to the playground. This can be symbolized with a connective called as a AND. This AND is a logical operator, AND is used. So, this can be symbolized as R and S, which is statement formula. This formula can be represented as in policy notifications. This policy notation is called as a infix notation. As I told in the first slide, there are three types of notations, infix, prefix, and post-fix. Let us see one by one. Infix notations, how they are represented? They are represented like this, operand one, followed by operator, followed by the operand two. Now, what is operator? Operators are plus, minus, multiplication, division. These are the arithmetic operators. The logical operators like AND, OR, conditional, biconditional, NAND, NOR, XOR, all these are the operators. So, whenever we write operator between two operands, that is called as a infix notation. So, operators are written in between their operands. This is a usual way we write expression. An expression such as, consider this expression, which is written in brackets, A multiplied by into bracket B plus C, bracket close divided by D, which is usual writing expression using plus multiplication and division. Now, here, how this expression is evaluated? It's what is the priority of the expression. Now, in mathematical expression, first of all, multiplication and divisions are evaluated first. Then, plus and division, plus and minus are evaluated. Out of that, the innermost, if suppose brackets are there, the innermost bracket will be evaluated first. So, in this example, we observe that B plus C is the innermost bracket. So, B plus C will be evaluated. So, first of all, add B and C together. That is, B plus C will be evaluated. The result of that is multiplied with A, that is, A multiplied by result of B plus C. Then, the result of this entire bracket is divided by D. This now, the expression is evaluated. Now, prefix notation. If you look at this, plus X, Y, this indicates that plus is the operator, followed by the two operands, X and Y. Means, in this case, first of all, operator, followed by the two operands. In fixed, first operand one, operator, then lastly, operand two. But, in the prefix, it is, first of all, operator followed by the two operands. Operands are written before their operands. Now, the same expression, the same expression, A into B plus C divided by D, can be written in prefix like this. First of all, divide, multiplication, A plus B, C and D. As for the post-fix operators, left to right and brackets are super plus operators act on the two nearest values on the right. We have again added totally unnecessary brackets. Means, saying that plus B, C is evaluated first. Then, result of that will be evaluated with A with a multiplication and result of this will be with D by the division operation. Now, the prefix notation, in the example, given in the previous slide, although the division is the first operator on the left side, it acts on the result of the multiplication. And so, the multiplication has to happen before the division. And similarly, addition has to happen before the multiplication, because they are stored in the brackets, because post-fix operators use values to their left. Any values involving computations will already have been calculated, and we go left to right. And so, the order of evolution of the operators is not disrupted in the way as a prefix expression. Post-fix notations. It is also known as a reverse-polish notation, and it is denoted as X, Y plus, indicating that X, Y are the operands, operand one, operand two, X is operand one, Y is operand two, and followed by the operator plus. Operators are written after the operands. The in-fix expression given above is equivalent to A, B, C plus, multiplication, division, D division. Now, operators act on the values immediately to the left of them. For example, the plus above uses the B and C. We can add totally unnecessarily brackets to make the explicit, like B, C plus first of all, then followed by the result of that with a multiplication with A, and the result of A multiplied by B, C plus, divided by D. Thus, the multiplication uses the two values immediately preceding A and the result of the addition. Similarly, the division uses the result of the multiplication of D. Take a minute and write the following statement into in-fix notations. Now, Ram is playing football, and Shyam is watching the television. Now, this is a compound statement. This is a compound statement. Now, what are the simple statements? The first simple statement is Ram is playing the football, and the second statement is Shyam is watching the television. These are the two statements connected by this and, A and D and. Let us take a minute and solve this. The answer, this can be symbolized. Ram playing football can be symbolized, say, with R. Shyam is watching the television with, say, S. Ram is playing football, and Shyam is watching the television. This can be symbolized with R and S, which is called the in-fix notation. The same can be written in in-fix is called as an and R S, and same can be written as in post-fixes R S and. Take a note, in all three versions, the operands occur in the same order and just the operators have to move to keep the meaning correct. This is particularly important for the asymmetric operators like subtraction and division. A minus B does not mean that the same as B minus A. The formula is equivalent to A B minus or minus A B in case of prefix. The latter to B A minus or minus B A. The B A minus is post-fix, and this minus B A is a prefix. These are the some in-fix, post-fix and prefix notations. Let us consider the first one. A into B plus C divided by D. Multiply A and B, divide C by D at the results. The same thing in post-fix it is written as A B's. Multiplication C D slash plus in prefix plus A B division C D. This is how the remaining expressions are encountered. These are the references. I hope you understood the polished notations. Thank you.