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Applied Mathematics · Class 11 Commerce

Ch 7Mathematical and Logical Reasoning — Class 11 Applied Mathematics, concept-first.

This concept map shows how the chapter fits together. It has two halves. Logical-reasoning applications include coding-decoding, relationships, classification and syllogisms. Mathematical statements are built and combined using the connectives NOT, OR and AND, the implications (if-then, if and only if) and quantifiers.

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Introduction

You've been solving problems your whole life. When you see a new type of question, you first figure out what it's asking, then decide which tools to use, then carry out the steps.

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

Concept Map

This concept map shows how the chapter fits together. It has two halves. Logical-reasoning applications include coding-decoding, relationships, classification and syllogisms.

7.1

Introduction

Every day, you make decisions based on facts, conditions, and rules — from choosing what to wear based on the weather to solving a puzzle.

7.2

Mathematical Statements

We begin by noticing that not every sentence in mathematics is a statement. A statement is a declarative sentence that is either true or false, but not both.

+Exercise 7.1i6 questions
  1. Q1Check whether the following sentence is a mathematically acceptable statement. Give reasons for your answer: 8 is less than 6.Free
  2. Q2Check whether the following sentence is a mathematically acceptable statement. Give reasons for your answer: Every set is a finite set.Free
  3. Q3Check whether the following sentence is a mathematically acceptable statement. Give reasons for your answer: The sun is a star.Preview
  4. Q4Check whether the following sentence is a mathematically acceptable statement. Give reasons for your answer: Mathematics is fun.Preview
  5. Q5Check whether the following sentence is a mathematically acceptable statement. Give reasons for your answer: There is no rain without clouds…Preview
  6. Q6Check whether the following sentence is a mathematically acceptable statement. Give reasons for your answer: How far is Chennai from here?Preview
7.3

Creating New Statements

We already know that a statement is a sentence that is either true or false, but not both. The real power of logic lies in taking one or more such statements and combining them to form entirely new on…

+Exercise 7.2i3 questions
  1. Q1For the following statement, determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer: The school is clos…Free
  2. Q2For the following statement, determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer: Two lines intersec…Preview
  3. Q3For the following statement, determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer: Students can take…Preview
7.4

Quantifiers

Quantifiers tell us how many objects in a set satisfy a given condition — they turn an open statement like " is even" into a definite proposition.

7.5

Implications-'If-then'

Conditional statements are the backbone of logical deduction — they tell us that if one thing happens, another must follow.

7.6

Implications 'If and Only If'

When a statement is true in both directions — if then and if then — we say holds if and only if holds.

7.7

Validating Statements

Statements in mathematics are not just sentences — they are claims that must be either true or false. But how do you decide whether a statement like "If , then " is actually valid? Validating a statem…

7.8(a)

Applications of Reasoning -- Categorical Syllogism

6 Q

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.

+Examples 7.8(a)i2 questions
  1. Example 1Statements: I. Some goats are vegetarians. II. All vegetarians are blessed. Conclusions: I. Some goats are blessed. II. At least some blesse…Free
  2. Example 2Statements: I. Some pictures are beds. II. All beds are trees. Conclusions: I. Some pictures are trees. II. At least some trees are beds. Gi…Preview
+Exercise 7.3i4 questions
  1. Q1Two statements are given below followed by two conclusions numbered (1) and (2). Take the given two statements to be true even if they seem…Free
  2. Q2Two statements are given below followed by two conclusions numbered (1) and (2). Take the given two statements to be true even if they seem…Free
  3. Q3Two statements are given below followed by two conclusions numbered (1) and (2). Take the given two statements to be true even if they seem…Preview
  4. Q4Two statements are given below followed by two conclusions numbered (1) and (2). Take the given two statements to be true even if they seem…Preview
7.8(b)

Applications of Reasoning -- Coding-Decoding

9 Q

Coding-decoding problems are a direct application of the logical reasoning you have already studied — they test your ability to spot a hidden rule or pattern that transforms one set of symbols into an…

+Examples 7.8(b)i5 questions
  1. Example 3If DPT is coded as EQU, then what is TRY?Free
  2. Example 4In a certain language, if BLOWN is coded as BLNOW then how will RIGHT be coded? a) HIRGT b) SJHIU c) GHIRT d) THIGRFree
  3. Example 5In a certain language, PAC is coded as 61, how will NEP be coded? a) 40 b) 66 c) 80 d) 46Preview
  4. Example 6If MADAM is coded as ✳?#?✳ and DOOM is coded as #%%✳ then LAD will be coded as ........... a) ?#% b) &?# c) ✳#/ d) ??#Preview
  5. Example 7If BRED is coded as #✳?% , then BREEZE will be coded as .........? a) #&%%?✳ b) ??%%#✳ c) %%%?^^ d) ???%#@Preview
+Exercise 7.4i4 questions
  1. Q1In a certain language, if CAMEL is coded as DBNFM then how will ROOM be coded? a) NPPQ b) SPPN c) PPON d) NQQPFree
  2. Q2If BLEPIN is coded as 987416, MATPIN is coded as 123416, then TABLE is coded as? a) 32987 b) 32897 c) 38987 d) 21987Free
  3. Q3In a certain language, 'hi mi si' means 'Air is life'. 'si ni zi' means 'Balloon of Air'. 'ci zi mi' means 'Life of PI'. Which of the follow…Preview
  4. Q4In a certain language, 321 means 'Glass of Tea'. 426 means 'Tea is Brown'. 796 means 'Trunks are Brown'. Which of the following represents '…Preview
7.8(c)

Applications of Reasoning -- Blood Relation

5 Q

Blood relation problems are a direct application of logical reasoning to real-life family structures. Instead of memorising arbitrary rules, you learn to trace relationships step by step, using precis…

+Examples 7.8(c)i2 questions
  1. Example 8Arun said, "Ishika is the daughter of my mother's daughter". How is Arun related to Ishika?Free
  2. Example 9Pointing to a man, Akshay said, "His son is my son's uncle". How is the man related to Akshay?Preview
+Exercise 7.5i3 questions
  1. Q1Pointing to a picture the man said, "The lady in the picture is my nephew's maternal grandmother." How is the lady in the picture related to…Free
  2. Q2Meenakshi is Kirti's sister. Kaavya is Kirti's mother. Dipesh is Kaavya's father. Esha is Dipesh's mother. Then, how is Meenakshi related to…Preview
  3. Q3P+Q means P is the brother of Q, R-S means R is the father of S, S/T means S is the sister of T, T x U means T is the mother of U. Which of…Preview
7.8(d)

Applications of Reasoning -- Odd Man Out

5 Q

Odd Man Out problems test your ability to spot the single element that breaks a hidden pattern. Instead of hunting for the answer blindly, you first identify the common property — a shared shape, numb…

+Examples 7.8(d)i2 questions
  1. Example 10Which one of the words given below is different? a - Mango b - Apple c - Potato d - Cherry e - BlackberryFree
  2. Example 11Find out the pair which is different. a - Cow and Buffalo b - Cock and Hen c - Horse and Mare d - Dog and Bitch e - Peacock and PeahenPreview
+Exercise 7.6i3 questions
  1. Q1Find the odd man out from the given alternatives. a. Insurance b. Provident Fund c. Salary d. SharesFree
  2. Q2Which number is the odd man out in the numbers 3, 5, 11, 14, 17, 21? a. 21 b. 17 c. 14 d. 3Preview
  3. Q3Find out the odd man out from the figures given below: four rectangular boxes (labelled a, b, c, d), each divided into a left portion filled…Preview
7.9

Practical Work Using Spread Sheet

Spreadsheets turn abstract logical reasoning into something you can see and test. By entering formulas like =IF(A15, "Pass", "Fail"), you directly apply the truth tables and conditional statements fro…