Statement in Logic.


Hello friends, Welcome to my blog mathstips4u.


I will give you tips and trick how to prepare for both HSC board exams and JEE Main Exam.In my last post we were discussed an introduction to Mathematical Logic. If you are new visitor or accidently came to this blob before reading this post, please read my previous video post. o
 In this post we are going to learn what is mean by Statement in Logic.Please watch my video till ends, at the end I will ask a few questions try to answer it in the comment. I will provide the answers in my next post. So let’s begin.Mathematical Logic.
First we shall see the difference between sentence and statement.Sentence is a group of words having some meaning.There are 4 types of sentences.1.   Imperative
2.   Interrogative
3.    Exclamatory
4.    Assertive We shall see the couple examples of each of type of sentences1.   Imperative
          1 Shut the door.          2. Please get me a book.2. Interrogative
          1.Do you like to see a film?          2. Do you exercise regularly?3.  Exclamatory     
1. Oh! What a beautiful sight it is!          2.What a heavy down pour!4. Declarative          1. Sky is blue.
          2. 6 is prime a number.         
        3. 2 + 3 = 6.
Out of these 4 types of sentences only declarative or assertive sentences are Statements which is either true or false but not simultaneously.
Statements are generally denoted by letters p, q, r, … etc.
e.g. 1) p: sky is blue     Truth value is T          2) q: 4 + 3 = 9         Truth value is F If a statement is true, then its truth value is True (T)
and if it is false then its truth value is False (F)Now we consider the following declarative sentences1.   X + 3 = 5. It is true if x = 2, it is false if x other than 2.2.   It is white in color. IF its milk then it is true and if it is coffee then it is false.  3.   Mathematics is an easy subject. May be true for you, and False for me.
In the first sentence we cannot say it is true or false unless we know the value of x.In second sentence we do not know what about we are talking.In third sentence the truth values vary from person to person.
Such declarative sentences are not statements they are called Open Sentences.
Finally, mathematical identities and formulae are always true statements.e.g. 1. X + 0 = X
2.     + x  = 13.   =  + 2ab +     These are true statements.So in this video we have seen what is meant by a statement.
Ex. Which of the following sentences are statements in logic? In case of statements, write down the truth value.1.   Today is Saturday.
2.   Work hard.
3.   Moon is a satellite.
4.   He likes coffee.
5.  3x +2 = 0, x = 2
6.   Do not disturb me.7.   Why you are angry?8.   May god bless you!
9.   Swimming is fun.
  is a complex number.Be touch with me. My next post is about connectives and compound statements. 

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