Question 12 Marks
If n(A) = 7, n(B) = 13, n(A ∩ B) = 4, then n(A ∪ B) = ?
Answer
View full question & answer→n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
= 7 + 13 – 4
n(A ∪ B) = 16
= 7 + 13 – 4
n(A ∪ B) = 16
Questions
2 Mark Question
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20 questions · self-marked practice — reveal the answer and mark yourself.
Question 22 Marks
Observe the Venn diagram and write the given sets U, A, B, A ∪ B and A ∩ B.
Answer
View full question & answer→U = {1,2, 3,4, 5, 7, 8, 9, 10, 11, 13}
A = {1, 2, 3, 5,7}
B = {1, 5, 8, 9, 10}
A ∪ B = {1,2, 3, 5, 7, 8, 9, 10}
A ∩ B = {1, 5}
A = {1, 2, 3, 5,7}
B = {1, 5, 8, 9, 10}
A ∪ B = {1,2, 3, 5, 7, 8, 9, 10}
A ∩ B = {1, 5}
Question 32 Marks
If M is any set, then write M ∪Φ and M ∩ Φ.
Answer
View full question & answer→Let M = {2, 3, 4, 8} and Φ = { }
∴ M ∪ Φ = {2, 3, 4, 8}
∴ M ∪ Φ = M Also, M ∩ Φ = { }
∴ M ∩ Φ = i(i
∴ M ∪ Φ = {2, 3, 4, 8}
∴ M ∪ Φ = M Also, M ∩ Φ = { }
∴ M ∩ Φ = i(i
Question 42 Marks
If n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, then n(A ∩ B) = ?
Answer
View full question & answer→n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
∴ 36 = 20 + 28 – n(A ∩ B)
∴ n(A ∩ B) = 20 + 28 – 36
∴ n(A ∩ B) = 12
∴ 36 = 20 + 28 – n(A ∩ B)
∴ n(A ∩ B) = 20 + 28 – 36
∴ n(A ∩ B) = 12
Question 52 Marks
Every student should take 9 triangular sheets of paper and one plate. Numbers from 1 to 9 should, be written on each triangle. Everyone should keep some numbered triangles in the plate. Now the triangles in each plate form a subset of the set of numbers from 1 to 9.
Look at the plates of Sujata, Hameed, Mukta, Nandini, Joseph with the numbered triangles. Guess the thinking behind selecting these numbers. Hence write the subsets in set builder form.
Look at the plates of Sujata, Hameed, Mukta, Nandini, Joseph with the numbered triangles. Guess the thinking behind selecting these numbers. Hence write the subsets in set builder form.
Answer
View full question & answer→Sujata:
$S=\{x \mid x=2 n-1, n \in N, x<9\}$
Hameed:
$f H=\{x \mid x=2 n, n \in N, x<9\}$
Mukta:
$M=\left\{x \mid x=n^2, n \in N, x \leq 9\right\}$
Nandini:
$N=\{x \mid x \in N, x \leq 9\}$
Joseph:
$J=\{x \mid x \text { is a prime number between } 1 \text { and } 9\}$
$S=\{x \mid x=2 n-1, n \in N, x<9\}$
Hameed:
$f H=\{x \mid x=2 n, n \in N, x<9\}$
Mukta:
$M=\left\{x \mid x=n^2, n \in N, x \leq 9\right\}$
Nandini:
$N=\{x \mid x \in N, x \leq 9\}$
Joseph:
$J=\{x \mid x \text { is a prime number between } 1 \text { and } 9\}$
Question 62 Marks
Set of students in a class and set of students in the same class who can swim, are shown by the Venn diagram.
Observe the diagram and draw Venn diagrams for the following subsets.
i. a. Set of students in a class
b. Set of students who can ride bicycles in the same class
ii. A set of fruits is given as follows.
U = {guava, orange, mango, jackfruit, chickoo, jamun, custard apple, papaya, plum}
Show these subsets.
A = fruit with one seed
B = fruit with more than one seed.
Answer
View full question & answer→i.
ii. A = {mango, jamun, plum}
B = {guava, orange, jackfruit, chickoo, custard apple, papaya}
Question 72 Marks
A = { x | x is a letter of the word ‘listen’.}
B = { y | y is a letter of the word ‘silent’.} verify that A=B.
B = { y | y is a letter of the word ‘silent’.} verify that A=B.
Answer
View full question & answer→A = { x | x is a letter of the word ‘listen’.} ∴ A = { l, i, s, t, e, n}
B = { y | y is a letter of the word ‘silent’.} ∴ B = { s, i, l, e, n, t}
Though the elements of set A and B are not in the same order but all the elements
are identical.
∴ A = B
B = { y | y is a letter of the word ‘silent’.} ∴ B = { s, i, l, e, n, t}
Though the elements of set A and B are not in the same order but all the elements
are identical.
∴ A = B
Question 82 Marks
Question 92 Marks
U = { 1, 3, 9, 11, 13, 18, 19}
B = {3, 9, 11, 13}
Find B' and draw the inference.
B = {3, 9, 11, 13}
Find B' and draw the inference.
Answer
B' = {1, 18, 19}
View full question & answer→B' = {1, 18, 19}
Question 102 Marks
U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 4, 6, 8, 10} Find A' And Draw The inference.
A = {2, 4, 6, 8, 10} Find A' And Draw The inference.
Answer
∴ A'= {1, 3, 5, 7, 9}
View full question & answer→∴ A'= {1, 3, 5, 7, 9}
Question 112 Marks
Observe the given Venn diagram and write the following sets.
i. A
ii. B
iii. A ∪ B
iv. U
v. A’
vi. B’
vii. (A ∪B )’
i. A
ii. B
iii. A ∪ B
iv. U
v. A’
vi. B’
vii. (A ∪B )’
Answer
View full question & answer→i. A = {x, y, z, m, n}
ii. B = {p, q, r, m, n}
iii. A ∪ B = {x, y, z, m, n, p, q, r }
iv. U = {x, y, z, m, n, p, q, r, s, t}
v. A’ = {p, q, r, s, t}
vi. B’ = {x, y, z, s, t}
vii. (A ∪ B )’ = {s, t}
ii. B = {p, q, r, m, n}
iii. A ∪ B = {x, y, z, m, n, p, q, r }
iv. U = {x, y, z, m, n, p, q, r, s, t}
v. A’ = {p, q, r, s, t}
vi. B’ = {x, y, z, s, t}
vii. (A ∪ B )’ = {s, t}
Question 122 Marks
If n(A) = 15, n(A ∪ B) = 29, n(A ∩ B) = 7, then n(B) = ?
Answer
View full question & answer→Here, n(A) = 15, n(A ∪ B) = 29, n(A ∩ B) = 7
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
∴ 29 = 15 + n(B) – 7
∴ 29 – 15 + 7 = n(B)
∴ n(B) = 21
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
∴ 29 = 15 + n(B) – 7
∴ 29 – 15 + 7 = n(B)
∴ n(B) = 21
Question 132 Marks
Let all the students of a class form a Universal set. Let set A be the students who secure 50% or more marks in Maths. Then write the complement of set A.
Answer
View full question & answer→Here, U = all the students of a class.
A = Students who secured 50% or more marks in Maths.
∴ A’= Students who secured less than 50% marks in Maths.
A = Students who secured 50% or more marks in Maths.
∴ A’= Students who secured less than 50% marks in Maths.
Question 142 Marks
A = {1, 3, 2, 7}, then write any three subsets of A.
Answer
View full question & answer→Three subsets of A:
i. B = {3}
ii. C = {2, 1}
iii. D= {1, 2, 7}
[Note: The above problem has many solutions. Students may write solutions other than the ones given]
i. B = {3}
ii. C = {2, 1}
iii. D= {1, 2, 7}
[Note: The above problem has many solutions. Students may write solutions other than the ones given]
Question 152 Marks
A = {x | x is prime number and 10 < x < 20} and B = {11,13,17,19}. Here A = B. Verify.
Answer
View full question & answer→A = {x | x is prime number and 10 < x < 20}
∴ A = {11, 13, 17, 19}
B = {11, 13, 17, 19}
∴ All the elements in set A and B are identical.
∴ A and B are equal sets, i.e. A = B
∴ A = {11, 13, 17, 19}
B = {11, 13, 17, 19}
∴ All the elements in set A and B are identical.
∴ A and B are equal sets, i.e. A = B
Question 162 Marks
Write the following sets using rule method.
i. A = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
ii. B= {6, 12, 18,24, 30,36,42,48}
iii. C = {S, M, I, L, E}
iv. D = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
v. X = {a, e, t}
i. A = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
ii. B= {6, 12, 18,24, 30,36,42,48}
iii. C = {S, M, I, L, E}
iv. D = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
v. X = {a, e, t}
Answer
View full question & answer→i. A = {x | v = n², n e N, n < 10}
ii. B = {x j x = 6n, n e N, n < 9}
iii. C = {y j y is a letter of the word ‘SMILE’} [Other possible words: ‘SLIME’, ‘MILES’, ‘MISSILE’ etc.]
iv. D = {z | z is a day of the week}
v. X = {y | y is a letter of the word ‘eat’}
[Other possible words: ‘tea’ or ‘ate’]
ii. B = {x j x = 6n, n e N, n < 9}
iii. C = {y j y is a letter of the word ‘SMILE’} [Other possible words: ‘SLIME’, ‘MILES’, ‘MISSILE’ etc.]
iv. D = {z | z is a day of the week}
v. X = {y | y is a letter of the word ‘eat’}
[Other possible words: ‘tea’ or ‘ate’]
Question 172 Marks
Write the following sets using listing method.
i. All months in the Indian solar year.
ii. Letters in the word ‘COMPLEMENT’.
iii. Set of human sensory organs.
iv. Set of prime numbers from 1 to 20.
v. Names of continents of the world.
i. All months in the Indian solar year.
ii. Letters in the word ‘COMPLEMENT’.
iii. Set of human sensory organs.
iv. Set of prime numbers from 1 to 20.
v. Names of continents of the world.
Answer
View full question & answer→i. A = {Chaitra, Vaishakh, Jyestha, Aashadha, Shravana, Bhadrapada, Ashwina, Kartika, Margashirsha, Paush, Magha, Falguna}
ii. X = {C, O, M, P, L, E, N, T}
iii. Y = {Nose, Ears, Eyes, Tongue, Skin}
iv. Z = {2, 3, 5, 7, 11, 13, 17, 19}
v. E = {Asia, Africa, Europe, Australia, Antarctica, South America, North America}
ii. X = {C, O, M, P, L, E, N, T}
iii. Y = {Nose, Ears, Eyes, Tongue, Skin}
iv. Z = {2, 3, 5, 7, 11, 13, 17, 19}
v. E = {Asia, Africa, Europe, Australia, Antarctica, South America, North America}
Question 182 Marks
Write any two sets by listing method and by rule method.
Answer
View full question & answer→i. A is a set of even natural numbers less than 10.
Listing method: A = {2, 4, 6, 8}
Rule method: A = {x | x = 2n, n e N, n < 5}
Listing method: A = {2, 4, 6, 8}
Rule method: A = {x | x = 2n, n e N, n < 5}
ii. B is a set of letters of the word ‘SCIENCE’. Listing method : B = {S, C, I, E, N}
Rule method: B = {x \ x is a letter of the word ‘SCIENCE’}
Question 192 Marks
Write the following symbolic statements in words.
i. $\frac{4}{3} \in Q$
ii. $-2 \notin N$
iii. $P=\{p \mid p$ is an odd number $\}$
i. $\frac{4}{3} \in Q$
ii. $-2 \notin N$
iii. $P=\{p \mid p$ is an odd number $\}$
Answer
View full question & answer→i. $\frac{4}{3}$ is an element of set $Q$.
ii. -2 is not an element of set $N$.
iii. Set $P$ is a set of all $p$ 's such that $p$ is an odd number.
ii. -2 is not an element of set $N$.
iii. Set $P$ is a set of all $p$ 's such that $p$ is an odd number.
Question 202 Marks
Write the following sets in roster form.
i. Set of even natural numbers
ii. Set of even prime numbers from 1 to 50
iii. Set of negative integers
iv. Seven basic sounds of a sargam (sur)
i. Set of even natural numbers
ii. Set of even prime numbers from 1 to 50
iii. Set of negative integers
iv. Seven basic sounds of a sargam (sur)
Answer
View full question & answer→i. A = { 2, 4, 6, 8,….}
ii. 2 is the only even prime number
∴ B = { 2 }
iii. C = {-1, -2, -3,….}
iv. D = {sa, re, ga, ma, pa, dha, ni}
ii. 2 is the only even prime number
∴ B = { 2 }
iii. C = {-1, -2, -3,….}
iv. D = {sa, re, ga, ma, pa, dha, ni}