1 Marks Question

Question 11 Mark

If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.
a is less that 6 and $\text{a} \in \text{Y}$

Answer

Given that: Y = {1, 2, 3, ....., 10}
{a | a is less than 6 and $\text{a}\in\text{Y}$} = {1, 2, 3, 4, 5}

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Question 21 Mark

If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.
$\text{a} \in \text{Y}$ but $\text{a}^2 \notin \text{Y}.$

Answer

Given that: Y = {1, 2, 3, ....., 10}
Since $1^2, 2^2, 3^2 \in \text{Y},$
$\{\text{a}:\text{a}\in\text{Y and}\text{ a}^2\notin\text{Y}\}=\{4,5,6,7,8,9,10\}$

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Question 31 Mark

Write the following sets in the roaster from.
C = {x | x is a positive factor of a prime number p}.

Answer

We have, C = {x | x is a positive of prime number p}
Since positive factors of a prime number are 1 and number itself, we have
C = {1, p}.

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Question 41 Mark

If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by.
n - 1.

Answer

Given that: X = {1, 2, 3}
$\{(\text{n}-1)|\text{n}\in\text{X}\}=\{0,1,2\}$

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Question 51 Mark

Given that N = {1, 2, 3, ..... , 100}. Then write.
The subset of N whose element are perfect square numbers.

Answer

We have, N= {1, 2, 3, 4, ....., 100}
Subset of N whose elements are perfect square = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}.

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Question 61 Mark

If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by.
$\frac{\text{n}}{2}$

Answer

Given that: X = {1, 2, 3}
$\Big\{\frac{\text{n}}{2}\Big|\text{n}\in\text{x}\Big\}=\Big\{\frac{1}{2},1,\frac{3}{2}\Big\}$

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Question 71 Mark

Write the following sets in the roaster from.
A = {x : x ∈ R, 2x + 11 = 15}

Answer

We have, A = {x : x ∈ R, 2x + 11 = 15}
2x + 11 = 15 ⇒ x = 2
$\therefore$ A = {2}

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Question 81 Mark

Let U be the set of all boys and girls in a school, G be the set of all girls in the school, B be the set of all boys in the school, and S be the set of all students in the school who take swimming. Some, but not all, students in the school take swimming. Draw a Venn diagram showing one of the possible interrelationship among sets U, G, B and S.

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Question 91 Mark

Write the following sets in the roaster from.
B = {x | x² = x, x ∈ R}.

Answer

We have, B = {x + x² = x, x ∈ R}
$\therefore$ x² = x
⇒ x² - x = 0
⇒ x(x - 1) = 0
⇒ x = 0, 1
$\therefore$ B = {0, 1}

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Question 101 Mark

If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by.
4n

Answer

Given that: X = {1, 2, 3}
$\{4\text{n}|\text{n}\in\text{X}\}=\{4,8,12\}$

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Question 111 Mark

If A and B are subsets of the universal set U, then show that.
$(\text{A}\cap\text{B})\subset\text{A}$

Answer

Let $\text{x}\in\text{A}\cap\text{B}$
$\Rightarrow \text{x}\in\text{A}$ and $\text{x}\in\text{B}$
$\Rightarrow \text{x}\in\text{A}$
So, $\text{A}\cap\text{B}\subset\text{A}.$

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Question 121 Mark

Given that N = {1, 2, 3, ..... , 100}. Then write.
The subset of N whose elements are even numbers.

Answer

We have, N= {1, 2, 3, 4, ....., 100}
Subset of N whose elements are even numbers = {2, 4, 6, 8, ....., 100}.

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Question 131 Mark

If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.
$\text{a}+1=6,\text{a} \in \text{Y}$

Answer

Given that: Y = {1, 2, 3, ....., 10}
$\{\text{a}|\text{a}+1=6,\text{a}\in\text{Y}\}={5}$

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Question 141 Mark

If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by.
n + 6.

Answer

Given that: X = {1, 2, 3}
$\{\text{n}+6|\text{n}\in\text{X}\}=\{7,8,9\}$

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