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Syllogisms: Quick Solving Tips By Bhagyashree Ghosh
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e What are Syllogisms? A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more premises (also called propositions) that are asserted or assumed to be true. The conclusion asserts no more than what is already contained, implicitly, in the premises. If it does, the syllogism is invalid . An important thing to be kept in mind is that one has to take the given statements to be true even if they seem to be at variance from commonly known facts.
Types of Premises . A premise is a statement which comprises of two terms: a subject and a predicate, connected by a relation. Subject is that about which something is said Predicate states something about the subject If another premise contains one of these terms (known as the common term), we can deduce a relation between the non- common terms.
Tvpe 1: All A are B The general representation of this premise is as shown below: O But there may be a case where A B, then this premise is true. A=B
Type 2: No A are B O The premise is represented as
Tvpe 3:Some A are B O It can be depicted as The Shaded portion denotes the premise. NOTE: Looking at this general representation, one may perceive that if"some A are B, then some A are not B,
e Type 3:Some A are B But the following cases can also imply 'Some A are B' All B are A. TAlaAd e are identica. O A and B are identical. B A-B We can see that in the case where (i) A is a subset of B or (ii) A B, the premise 'some A are not B' does not hold true.
Type 4 : Some A are not B The premise is represented in two ways OR