Notes
IIT Madras
Mathematics 🧮
Activity Questions 1.5

Activity Questions 1.5

Question 1 Which of the following is a correct representation of set comprehension?

○ {x ; x ∈ ℕ, x is even}

○ {x | x ∈ ℕ, x is even}

○ {x is even | x ∈ ℕ | x}

○ {x is even ; x ∈ ℕ, x}

Solution

Question 2 Which of the following is the set of natural numbers that are multiples of 3 or 5?

○ {x | x ∈ ℕ, x mod 3 = 0 and x mod 5 = 0}

○ {x | x ∈ ℤ, x mod 3 = 0 or x mod 5 = 0}

○ {x | x ∈ ℤ, x mod 3 = 0 and x mod 5 = 0}

○ {x | x ∈ ℕ, x mod 3 = 0 or x mod 5 = 0}

Solution

Context for Questions 3-6 The image provides context about students from Madras University participating in SCHROETER sports fest:

Student Set: {Abbas, Akhil, Aditya, Balachandra, Bhuvan, Chidambaram, Charan, Kiran, Dayal, Deepak, Jaivardhan, Nithin, Sunil, Karthik, Rakesh}

Sport Assignments:

Volleyball: {Akhil, Charan, Deepak, Sunil, Karthik, Rakesh}

Basketball: {Charan, Rakesh, Kiran, Chidambaram, Balachandra}

Cricket: {Abbas, Akhil, Aditya, Bhuvan, Charan, Dayal, Deepak, Kiran, Jaivardhan, Nithin, Rakesh}

Question 3 Which of the following sets represents students from Madras University who play both cricket and basketball?

○ {Abbas, Akhil, Rakesh}

○ {Bhuvan, Charan, Dayal, Kiran}

○ {Kiran, Charan, Rakesh}

○ {Aditya, Jaivardhan, Nithin, Rakesh}

Solution

Question 4 What is the number of students who play all the three sports?

○ 1

○ 2

○ 3

○ 4

Solution

Q5. Which of the following set represents the students from Madras University who play volleyball but not cricket?

○ {Akhil, Rakesh, Sunil, Karthik}

○ {Sunil, Karthik}

○ {Deepak, Sunil, Bhuvan, Dayal, Nithin}

○ {Abbas, Aditya, Bhuvan, Dayal, Kiran, Jaivardhan, Nithin}

Solution

Question 6 Which of the following sets represent the students from Madras University who are not playing cricket?

○ {Dayal, Deepak, Kiran, Jaivardhan}

○ {Rakesh, Kiran, Chidambaram, Balachandra}

○ {Bhuvan, Jaivardhan, Sunil, Chidambaram}

○ {Sunil, Chidambaram, Karthik, Balachandra}

Solution

Context

The image provides two sets representing items required for different exams:

Exam A items: {Hall ticket, Pen, Calculator, Ruler, Pencil}

Exam B items: {Compass, Pencil, Drafter, Ruler, Eraser, Sharpener, Hall ticket}

Q7. If exams A and B are going to be conducted simultaneously, then what are the items that are required to be carried by the student to the exam centre?

○ {Hall ticket, Ruler, Pencil, Eraser, Sharpener, Pen, Drafter, Compass, Calculator}

○ {Calculator, Ruler, Pencil, Hall ticket, Pen, Paper, Compass, Drafter}

○ {Pen, Calculator, Pencil, Hall ticket, Ruler, Compass, Drafter, Eraser}

○ {Ruler, Pencil, Compass, Drafter, Eraser, Sharpener, Hall ticket, Calculator}

Solution

Q8. If a student forgets to bring her Calculator, which exam will she not be allowed to write?

○ Exam B

○ She can write both the exams

○ Exam A

○ None of the above

Solution

Activity Questions 1.4construction of subsets and set operation

Related Chapters 📂

  • A Quick Introduction to Variables

    01 A Quick Introduction to Variables

    In Python, a variable is essentially a name or a label that refers to a value or stored data. You can think of a variable as a basket in real life used to keep track of information in your program. Variables temporarily store data in the computer’s memory. Variables are created when they are first assigned a value. An assignment statement creates a new variable and gives it a value. For example, price = 10 creates a variable named price and assigns it the integer value 10. Similarly, x = 6 creates a variable x with the value 6.

  • Activity Questions 1.1 🧠

    02 Activity Questions 1.1

    1. Below is a list of numbers: 22, -17, 47, -2000, 0, 1, 43, 1729, 6174, -63, 100, 32, -9. How many natural numbers are there in the given list? a) 6 b) 7 c) 8 d) 9 Solution Based on the sources, the set of natural numbers is denoted by N. This set includes 0, 1, 2, 3, 4, 5, and so on. The sources explicitly state that whenever they are talking about natural numbers, it always includes a 0, even though some books may not. Natural numbers are primarily used for counting.

  • Activity Questions 1.1

    03 Activity Questions 1.1

    “The cafe was like a battleship stripped for action.” The figure of speech used here is ___. Drawing on the information from the sources discussing figures of speech:

  • Activity Questions 1.10 🧠

    04 Activity Questions 1.10

    Answer the questions 1-3, based on following information: Let A = {x|x ∈ ℕ, x < 10 and x is odd} B = {y|y ∈ ℕ, y is a perfect square and 15 < y < 40} Q1. Which of the following is a subset of B × A? ○ {(36, 3), (25, 5), (36, 6)} ○ {(1, 25), (6, 36), (7, 25), (3, 36)} ○ {(16, 5), (25, 9), (36, 3), (16, 1)}

  • Activity Questions 1.11 🧠

    05 Activity Questions 1.11

    Q1. If Dom(f) = {x ∈ ℝ, f(x) ∈ ℝ} defined by f(x) = (x + 12)/(4x - 8), then the domain of the function f is ______ ○ ℝ ○ ℝ \ {1/4} ○ ℝ \ {-12} ○ ℝ \ {2} Solution Q2. The product of the minimum value of the function f(x) = 9|x| - 8 and the maximum value of the function g(x) = 11 - |x + 8| is ______

  • Activity Questions 1.2

    06 Activity Questions 1.2

    Q1. Which among the following use alliteration in its name? a) Kolkata Knight Riders b) Peter Parker c) Big Billion Days d) All of the above Based on the information in the sources, alliteration is a literary device where the first sounds of two adjacent words or phrases are similar or the same. This repetition of the initial sound is used to make language more impactful and rhythmic. Examples from the sources include:

  • Activity Questions 1.2 🧠

    07 Activity Questions 1.2

    1. Which of the following option(s) is(are) true? Solution Based on the sources and our conversation history, we can determine which of the given inequalities between fractions are true by finding a common denominator and comparing the numerators. Rational numbers, which include fractions, can be written in the form p/q. To compare two fractions which have different denominators, there is no way to directly compare them. The only way is to convert them into equivalent fractions such that they have the same denominator. A number that is a multiple of both denominators can be used as the common denominator. Once the denominators are the same, you can add the numerators, or in this case, compare them.

  • Activity Questions 1.3

    08 Activity Questions 1.3

    1. Which among the following sentences use discourse markers to express opinion Solution Drawing on the information in the sources, discourse markers are words or phrases that can be used to help structure conversation or express the speaker’s attitude or viewpoint. They can appear at the beginning of a sentence and take the entire sentence into their scope.