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Applied Mathematics · Ch 7 — Mathematical and Logical Reasoning

Applications of Reasoning -- Categorical Syllogism

7.8(a)

Applications of Reasoning -- Categorical Syllogism

A categorical syllogism is a structured argument made of three statements: two premises and a conclusion, each built from categories (sets) linked by words like all, no, or some. The goal is to test whether the conclusion follows necessarily from the premises — not whether it is factually true, but whether the reasoning is airtight. For example, if all AA are BB and all BB are CC, then all AA must be CC; this is valid. Understanding this form sharpens your ability to spot logical g …

Figure 7.1A Venn diagram for the syllogism statement 'All A are B': the circle for A lies entirely inside the circle for B
Fig. 7.1 — A Venn diagram for the syllogism statement 'All A are B': the circle for A lies entirely inside the circle for B

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

'All A are B': A's circle lies entirely wit …

Figure 7.2A Venn diagram for the syllogism statement 'No A are B': the circles for A and B do not overlap
Fig. 7.2 — A Venn diagram for the syllogism statement 'No A are B': the circles for A and B do not overlap

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

'No A are B': the two circles are di …