Activity Questions 1.6

Q1. Which of the following sets is(are) infinite?

Set of all Indian Nobel laureates

Set of squares of all odd natural numbers

Set of all countries in the world

Set of all leap years

Q2. Which of the following set comprehension defines real numbers in interval [2, 0) ∪ (4, 8]?

○ {r | r ∈ ℝ, -2 ≤ r < 8}

○ {r | r ∈ ℝ, -2 ≤ r < 0 and 4 < r ≤ 8}

○ {r | r ∈ ℝ, -2 ≤ r < 0 or 4 < r ≤ 8}

○ {r | r ∈ ℝ, -2 ≤ r ≤ 0 and 4 ≤ r ≤ 8}

Q3. Which of the following set comprehensions define squares of first 100 natural numbers?

□ {n | n ∈ ℕ, √n ∈ ℕ and n < 100}

□ {n² | n ∈ ℕ, n < 100}

□ {n | n ∈ ℕ, √n ∈ ℕ and n < 10000}

□ {n² | n ∈ ℕ, n < 10000}

Q4. Which of the following statement(s) is(are) true?

□ Empty set contains only one element i.e. ∅.

□ Set with n elements has 2ⁿ⁻¹ subsets

□ Empty set is an element in the power set of a set

□ Power set is a set of all the subsets of a set

Q5. Which of the following intervals are subsets of [2,3]?

□ ((0, 2.3] ∪ (2.3, 3]) ∩ (0, 2.3)

□ ((2, 2.5] ∪ (2.5, 4]) \ (0, 2.3)

□ ((2, 2.5] ∪ (2.5, 4]) ∩ (0, 3)

□ ((0, 2.3] ∪ (2.2, 3]) \ (0, 2.3)

Q6. Let M be the set of all real numbers that are strictly greater than 6 or strictly less than -6. How can we represent B in set comprehension form, where B is a subset of M and has only integers as elements?

○ B = {z | z ∈ ℤ, z ∈ [-6, 6]}

○ B = {z | z ∈ ℤ, z ∈ (-6, 6)}

○ B = {z | z ∈ ℤ, z ∈ (-∞, -6] ∪ [6, ∞)}

○ B = {z | z ∈ ℤ, z ∈ (-∞, -6] ∪ [6, ∞)}

Q7. Two finite sets A and B are such that the total number of subsets of A is 56 more than the total number of subsets of B. What are the cardinalities of A and B respectively?

○ 6, 3

○ 8, 4

○ 7, 1

○ 8, 3