Advertisements
Advertisements
Question
Determine whether the following statement is true or false. Justify your answer.
For all sets A, B, and C, A – (B – C) = (A – B) – C
Options
True
False
Advertisements
Solution
This statement is False.
Explanation:
From the Venn Diagrams
A – (B – C) ≠ (A – B) – C
APPEARS IN
RELATED QUESTIONS
Identify whether the following is set or not? Justify your answer.
A team of eleven best-cricket batsmen of the world.
Identify whether the following is set or not? Justify your answer.
The collection of all even integers.
List all the elements of the following set:
B = `{x : x "is an integer", -1/2 < x < 9/2}`
List all the elements of the following set:
D = {x : x is a letter in the word “LOYAL”}
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
Describe the following sets in Roster form:
{x : x is a prime number which is a divisor of 60}
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:
\[B = \left\{ x: x = \frac{1}{2n - 1}, 1 \leq n \leq 5 \right\}\]
List all the elements of the following set:
D = {x : x is a vowel in the word "EQUATION"}
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a \right\} \in \left\{ a, b, c \right\}\]
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a, b \right\} \subset \left\{ a, \left\{ b, c \right\} \right\}\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ c, d \right\} \in A\]
Let A = {a, b, {c, d}, e}. Which of the following statements are false and why?
\[\left\{ a, b, e \right\} \in A\]
Let\[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true?
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? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\]
Write down all possible subsets of each of the following set:
{a, b, c},
Prove that:
\[A \subseteq B, B \subseteq C \text{ and } C \subseteq A \Rightarrow A = C .\]
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
10 _____ A
Describe the following set in Roster form
A = {x/x is a letter of the word 'MOVEMENT'}
Describe the following set in Set-Builder form
{0}
Describe the following set in Set-Builder form
{0, –1, 2, –3, 4, –5, 6, ...}
If A = {x/6x2 + x – 15 = 0}, B = {x/2x2 – 5x – 3 = 0}, C = {x/2x2 – x – 3 = 0} then find (A ∪ B ∪ C).
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 B but not Chemical A
There are 260 persons with skin disorders. If 150 had been exposed to the chemical A, 74 to the chemical B, and 36 to both chemicals A and B, find the number of persons exposed to Chemical A or Chemical B
Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:
n + 5 = 8
Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:
n is greater than 4
Write the following sets in the roaster from:
B = {x | x2 = x, x ∈ R}
Write the following sets in the roaster from:
C = {x | x is a positive factor of a prime number p}
In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows:
French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study French only
In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows:
French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study French and English but not Sanskrit
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 ______.
Let S = {x | x is a positive multiple of 3 less than 100}
P = {x | x is a prime number less than 20}. Then n(S) + n(P) is ______.
The set {x ∈ R : 1 ≤ x < 2} can be written as ______.
State True or False for the following statement.
Let sets R and T be defined as
R = {x ∈ Z | x is divisible by 2}
T = {x ∈ Z | x is divisible by 6}. Then T ⊂ R
