If set A = { 2, 3, 4, 5, 6 }, state which of the following statements are true and which are false:
(i) 2 ∈ A
(ii) 5, 6 ∈ A
(iii) 3, 4, 7 ∈ A
(iv) 2, 8 ∈ A
Answer
A = { 2, 3, 4, 5, 6 }
(i) 2 is a member of A.
True
(ii) Both 5 and 6 are members of A.
True
(iii) 3 and 4 are members of A, but 7 is not a member of A.
False
(iv) 2 is a member of A, but 8 is not a member of A.
False
If set B = { 4, 6, 8, 10, 12, 14 }, state which of the following statements are correct and which are wrong:
(i) 5 ∈ B
(ii) 12 ∈ B
(iii) 14 ∈ B
(iv) 9 ∈ B
(v) B is the set of even numbers between 2 and 16.
(vi) 4, 6 and 10 are the members of the set B.
Also, write the wrong statements correctly.
Answer
B = { 4, 6, 8, 10, 12, 14 }
(i) 5 is not a member of B.
Wrong; the correct statement is 5 ∉ B.
(ii) 12 is a member of B.
Correct
(iii) 14 is a member of B.
Correct
(iv) 9 is not a member of B.
Wrong; the correct statement is 9 ∉ B.
(v) The even numbers between 2 and 16 are 4, 6, 8, 10, 12 and 14, which are exactly the elements of B.
Correct
(vi) 4, 6 and 10 are all members of B.
Correct
State whether true or false:
(i) Sets { 4, 9, 6, 2 } and { 6, 2, 4, 9 } are not the same.
(ii) Sets { 0, 1, 3, 9, 4 } and { 4, 0, 1, 3, 9 } are the same.
(iii) Sets { 5, 4 } and { 5, 4, 4, 5 } are not the same.
(iv) Sets { 8, 3 } and { 3, 3, 8 } are the same.
(v) Collection of vowels used in the word 'ALLAHABAD' forms a set.
(vi) If P is the set of letters in the word 'ROOP'; then P = { p, o, r }
(vii) If M is the set of letters used in the word 'MUMBAI', then: M = { m, u, b, a, i }
Answer
(i) The two sets have the same elements 4, 9, 6 and 2. A change in order does not change a set, so they are the same. Hence, the statement that they are not the same is
False
(ii) Both sets have the same elements 0, 1, 3, 9 and 4. So, they are the same.
True
(iii) Repetition of elements does not change a set, so { 5, 4 } and { 5, 4, 4, 5 } are the same. Hence, the statement that they are not the same is
False
(iv) Repetition of elements does not change a set, so { 8, 3 } and { 3, 3, 8 } are the same.
True
(v) The collection of vowels in 'ALLAHABAD' is well defined (the only vowel used is A). So, it forms a set.
True
(vi) The letters in the word 'ROOP' are R, O, O, P. Writing each letter only once, the set of letters is { r, o, p } = { p, o, r }.
True
(vii) The letters in the word 'MUMBAI' are M, U, M, B, A, I. Writing each letter only once, M = { m, u, b, a, i }.
True
Write the set containing:
(i) the first five natural numbers.
(ii) the three types of angles.
(iii) the three types of triangles based on the length of their sides.
(iv) the members of your family.
(v) the first six consonants of the English alphabet.
(vi) the first four vowels of the English alphabet.
(vii) the names of any three Prime Ministers of India.
Answer
(i) The first five natural numbers are 1, 2, 3, 4 and 5.
The required set = { 1, 2, 3, 4, 5 }
(ii) The three types of angles (based on measure) are acute angle, right angle and obtuse angle.
The required set = { acute angle, right angle, obtuse angle }
(iii) The three types of triangles based on the length of their sides are scalene triangle, isosceles triangle and equilateral triangle.
The required set = { scalene triangle, isosceles triangle, equilateral triangle }
(iv) The members of your family form a well-defined collection.
The required set = { Write the name of each member of your family }
(v) The first six consonants of the English alphabet are b, c, d, f, g and h.
The required set = { b, c, d, f, g, h }
(vi) The first four vowels of the English alphabet are a, e, i and o.
The required set = { a, e, i, o }
(vii) Three Prime Ministers of India are Indira Gandhi, Atal Bihari Vajpayee and Dr. Manmohan Singh.
The required set = { Indira Gandhi, Atal Bihari Vajpayee, Dr. Manmohan Singh }
(a) Write the members (elements) of each set given below:
(i) { 3, 8, 5, 15, 12, 7 }
(ii) { c, m, n, o, s }
(b) Write the sets whose elements are:
(i) 2, 4, 8, 16, 64 and 128
(ii) 3, 5, 15, 45, 75 and 90
Answer
(a)
(i) The members of the set { 3, 8, 5, 15, 12, 7 } are
3, 8, 5, 15, 12 and 7.
(ii) The members of the set { c, m, n, o, s } are
c, m, n, o and s.
(b)
(i) The set whose elements are 2, 4, 8, 16, 64 and 128 is
{ 2, 4, 8, 16, 64, 128 }
(ii) The set whose elements are 3, 5, 15, 45, 75 and 90 is
{ 3, 5, 15, 45, 75, 90 }
(i) Write the set of letters used in the word 'BHOPAL'.
(ii) Write the set of vowels used in the word 'BENGAL'.
(iii) Write the set of consonants used in the word 'HONG KONG'.
Answer
(i) The letters used in the word 'BHOPAL' are B, H, O, P, A, L.
The required set = { b, h, o, p, a, l }
(ii) The vowels used in the word 'BENGAL' are E and A.
The required set = { e, a }
(iii) The letters in the word 'HONG KONG' are H, O, N, G, K, O, N, G. The consonants among these are H, N, G, K, N, G. Writing each consonant only once, we get H, N, G, K.
The required set = { h, n, g, k }