Activity Questions 1.4
Q1. Which of the following sets are same?
(i) {Ankitha, Keerthana, Raju, Suresh}
(ii) {Raju, Ankitha, Keerthana, Raju, Ankitha, Suresh}
(iii) {Keerthana, Suresh, Dheeraj, Raju, Ankitha}
(iv) {Suresh, Raju, Ankitha, Keerthana}
(v) {Dheeraj, Raju, Soumya, Keerthana}
a) (i) and (ii)
b) (iii),(iv) and (v)
c) (i) and (iv)
d) (i),(ii) and (iv)
Solution
Q2. Suppose X = {3, π, Tiger, Ball, -40, Dhoni}. Which of the following statement(s) is(are) true about X?
a) X is not a set because a collection of names of persons and numbers together will not be considered a set
b) X is not a set because “π” cannot be an element of a set.
c) X is a set because X contains items that are from more than two categories
d) X is a set because it is a collection of different well-defined items
Solution
Q3. Which of the following sets is a subset of the set of prime numbers?
○ {2, 3, 5, 8, 11}
○ {3, 5, 7, 11}
○ {2, 5, 7, 27}
○ {5, 9}
Solution
Q4. Which of the following statement(s) is(are) false?
□ Venn diagrams are pictorial representations of sets.
□ Every set is a subset of itself.
□ X ⊆ Y implies that X is a proper subset of Y.
□ Empty set contains only one element i.e. ∅.
Solution
Q5. Which of the following are empty sets?
Set of all perfect squares between 45 and 50
Set of all integers which are both even and odd
Set of all years having 366 days
Set of all prime numbers divisible by 2
Solution
Q6. If X = {a, b, c}, then the power set P(X) =
● {∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
○ {{a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
○ {∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}}
○ {{a}, {b}, {c}, {a, b}, {a, c}, {b, c}}
Solution
Q7. Let M be the set of all days in a week whose starting letter is either ‘S’ or ‘T’, and N be the set of all months in a year whose ending letter is ‘Y’. What are the cardinalities of M and N respectively?
○ 4, 3
○ 3, 4
○ 4, 4
○ 3, 3
Solution
Related Chapters 📂
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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.
🧠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.
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:
🧠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)}
🧠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 ______
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:
🧠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.
🧠08 Activity Questions 1.3
1. Which of the following statement(s) is(are) false? a) The sum of two natural numbers is always a natural number b) The difference between two integers is always an integer c) The product of two rational numbers is always a real number d) The product of two irrational numbers is always an irrational number Solution The statement that is false is: