SM1001905_Chapter-11_Connectives.pdf - CHAPTER \u2013 11 CONNECTIVES There have been some questions coming in entrance exams based on logical statements

SM1001905_Chapter-11_Connectives.pdf - CHAPTER u2013 11...

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Triumphant Institute of Management Education Pvt. Ltd. (T.I.M.E.) HO:95B, 2ndFloor, Siddamsetty Complex, Secunderabad – 500 003.Tel : 040–27898195 Fax : 040–27847334 email : [email protected]website : SM1001905/78 CHAPTER – 11CONNECTIVESThere have been some questions coming in entrance exams based on logical statements and logical connectives. A proper understanding of some basics in Logic will make answering such questions very easy. These questions can be answered easily and very quickly on the basis of some of the basics that we will look at in the following sections. Also, please note that these basics are useful not just for questions asked in CAT but are useful for other varieties of questions that you may come across in other entrance exams as well. In Logic, we deal with statements that are essentially sentences in the English language. However, in Logic we are not interested in or worried about the factual correctness of the sentence. We are interested only in the Logical “truthfulness” of the statements. For example, consider the statement: “If the sun rises in the west, then the moon rises in the north.” Here, we are not concerned with whether the sun rises in the east or west or with the direction in which the moon rises. We will only look at whether the moon will rise in the north or not depending on whether the part of the statement “The sun rises in the west” is true or not. If we are given that the sun rises in the west (which, incidentally, is factually incorrect), we can then conclude that the moon rises in the north (which again does not concern with the direction in which the moon actually rises). We can represent statements in Logic using symbols like p, q, etc, the way we represent variables/unknowns in Algebra using symbols like x, y, z, etc. Statements like “I will go for a movie”, “It is a sunny day”, etc are called simple statements. When two or more such simple statements are connected together to form a single statement, such a statement is called a compound statement. The simple statements are combined using logical connectives to form compound statements. We should know some of the important logical operators/connectives to be able to effectively tackle questions that involve compound statements and logical operations on compound statements. Negation (“NOT”) Any statement can be negated by using the words “not” or “no.” In layman’s language, negation is like the opposite of a statement. For example, the negation of the statement “It is raining” is “It is NOT raining.” The negation of the statement “He will pass the exam” is “He will not pass the exam.” This is equivalent to saying “He will fail in the exam.” So, when you are looking at negating the given statement, you should keep in mind the English equivalents of the statements also.
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