Advertisements
Advertisements
Question
State which of the following statements is true and which is false. Justify your answer.
496 ∉ {y | the sum of all the positive factors of y is 2y}.
Options
True
False
Advertisements
Solution
This statement is False.
Explanation:
Given that: 496 ∉ {y | the sum of all the positive factors of y is 2y}
∴ The positive factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496.
∴ The sum of all the positive factors of 496.
= 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 + 496
= 2 × 496
= 992
Hence, the given statement is false.
APPEARS IN
RELATED QUESTIONS
Identify whether the following is set or not? Justify your answer.
The collection of ten most talented writers of India.
Write the following set in roster form:
A = {x : x is an integer and –3 ≤ x < 7}
Write the following set in roster form:
F = The set of all letters in the word BETTER
Write the following set in the set-builder form:
{2, 4, 8, 16, 32}
Write the following set in the set-builder form:
{1, 4, 9, ....., 100}
Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
| (i) | {1, 2, 3, 6} | (a) | {x : x is a prime number and a divisor of 6} |
| (ii) | {2, 3} | (b) | {x : x is an odd natural number less than 10} |
| (iii) | {M, A, T, H, E, I, C, S} | (c) | {x : x is natural number and divisor of 6} |
| (iv) | {1, 3, 5, 7, 9} | (d) | {x : x is a letter of the word MATHEMATICS} |
Which of the following collection are sets? Justify your answer:
The collection of difficult topics in mathematics.
If A = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], then insert the appropriate symbol ∈ or ∉ in each of the following blank space:
4 ...... A
If A = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], then insert the appropriate symbol ∈ or ∉ in each of the following blank space:
12 ...... A
If A = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], then insert the appropriate symbol ∈ or ∉ in each of the following blank space:
0 ...... A
Describe the following sets in Roster form:
{x : x is a prime number which is a divisor of 60}
Describe the following sets in Roster form:
The set of all letters in the word 'Better'.
Describe the following sets in set-builder form:
{5, 25, 125 625}
List all the elements of the following sets:
\[A = \left\{ x: x^2 \leq 10, x \in Z \right\}\]
List all the elements of the following set:
\[C = \left\{ x: x \text{ is an integer }, - \frac{1}{2} < x < \frac{9}{2} \right\}\]
List all the elements of the following set:
D = {x : x is a vowel in the word "EQUATION"}
Write the set \[\left\{ \frac{1}{2}, \frac{2}{5}, \frac{3}{10}, \frac{4}{17}, \frac{5}{26}, \frac{6}{37}, \frac{7}{50} \right\}\] in the set-builder form.
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[\left\{ 1 \right\} \in A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[2 \subset A\]
Let \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\] Which of the following are true? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\]
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
8 ____ A
Describe the following set in Roster form
B = `{x//x "is an integer", -3/2 < x < 9/2}`
Describe the following set in Set-Builder form
`{1/2, 2/5, 3/10, 4/17, 5/26, 6/37, 7/50}`
From amongst 2000 literate individuals of a town, 70% read Marathi newspapers, 50% read English newspapers and 32.5% read both Marathi and English newspapers. Find the number of individuals who read neither Marathi and English newspaper
There are 260 persons with skin disorders. If 150 had been exposed to chemical A, 74 to chemical B, and 36 to both chemicals A and B, find the number of persons exposed to Chemical A but not Chemical B
Write the following interval in Set-Builder form
[– 3, 4)
A college awarded 38 medals in volleyball, 15 in football, and 20 in basketball. The medals awarded to a total of 58 players and only 3 players got medals in all three sports. How many received medals in exactly two of the three sports?
Answer the following:
Write down the following set in set-builder form
{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
Write the following sets in the roaster form:
E = `{w | (w - 2)/(w + 3) = 3, w ∈ R}`
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed in English and Mathematics but not in Science.
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed in Mathematics and Science but not in English
In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Find the number of students who play neither?
Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis. Then ______.
The set {x ∈ R : 1 ≤ x < 2} can be written as ______.
If A and B are any two sets, then A – B is equal to ______.
Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B.
