Question 11 Mark
Let A = {a, b, {c, d}, e}. Then the following statements is false and why?
$\phi\in \text{A}$
AnswerFalse.Explanation:
$\because\oint$ is a subset and not an element of A.
View full question & answer→Question 21 Mark
The given statements is corect? Write a correct form of the given incorrect statements.$\{\text{b, c}\}\subset\{\text{a},\{\text{b, c}\}\}$
AnswerFalse.Explanation:
$\because$ {a, b,} is an element and not a subset of {a, {b, c}}. The correct form is $\{\text{b, c}\}\in\{\text{a},\{\text{b, c}\}\}.$
View full question & answer→Question 31 Mark
Write the following statement are true? Justify your answer.
The set of all rectangles is contaied in the set of all squares.
AnswerThe given statement is 'False'.Explanation:
$\because$ A rectangle need not be a square.
View full question & answer→Question 41 Mark
The given statements is correct? Write a correct form of the give incorrect statement.
$\text{a}\subset\{\text{a, b, c}\}$
AnswerFalse.Explanation:
The correct statement is $\text{a}\in \text{\{a, b, c}\}.$
View full question & answer→Question 51 Mark
Let A = {{1, 2,3}, {4, 5}, {6, 7, 8}}. Then the following is true or false:
$\{1,2,3\}\subset \text{A}.$
AnswerFalse.Explanation:
$\because$ {1,2,3} is not a subset of A, it is an element of A.
View full question & answer→Question 61 Mark
The following stetements are true? Given reason to support your answer.
{a, b, c} and {1, 2, 3} are equivalent are true or false.
AnswerTrue.Explanation:
$\because$ equivalent sets have the same cardinal number.
View full question & answer→Question 71 Mark
State whether the following statements are true or false:
{a} $\in$ {a, b, c}
AnswerFalse.Explanation:
$\because$ {a} is a subset of the set {a, b, c} and not an element.
View full question & answer→Question 81 Mark
State whether the following statements are true or false:
{a, b} = {a, a, b, b, a}
AnswerTrue.Explanation:
$\because$ repetition is not allowed in a set.
View full question & answer→Question 91 Mark
Let $\text{A}=\{\phi,\{\phi\},1\{1,\phi\},2\}.$ Then the statement is true?
$\{\{2\},\{1\}\}\not\subset\text{A}.$
AnswerTrue.Explanation:
$\because$ {{2},{1}} is not a subset of A.
View full question & answer→Question 101 Mark
Let $\text{A}=\{\phi,\{\phi\},1\{1,\phi\},2\}.$ Then the statement is true?
$\{2,\phi\}\subset\text{A}.$
AnswerTrue.Explanation:
$\because$ {2, {$\phi$}} is a subset of A.
View full question & answer→Question 111 Mark
The given statements is corect? Write a correct form of the given incorrect statements.
$\phi\subset \{\text{a, b, c}\}$
AnswerTrue.Explanation:
$\because$ empty set $\phi$ is a subset of every set.
View full question & answer→Question 121 Mark
State whether the following statements are true or false:
The set {x : x + 8 = 8} is the null set.
AnswerFalse.Explanation:
$\because$ the set {x : x + 8 = 8} is the single ton set {0} which is not the null set $\oint.$
View full question & answer→Question 131 Mark
State whether the following statements are true or false:
a $\subset$ {b, c, a}
AnswerFalse.Explanation:
$\because$ a is an element and not a subset of the set {b, c, a}.
View full question & answer→Question 141 Mark
Write the following statement are true? Justify your answer.
The set of all real number is contained in the set of all complex numbers.
AnswerThe given statement is 'True'.Explanation:
If z is a complex number, then it can be written as z = x + iy, where x and y are real numbers and are called the real and imaginary parts of the complex number z. If x is a real number, then x = x + i, $0\in \text{C},$ where C is the set of complex numbers. Thus $\text{x}\in\text{R}\Rightarrow\text{x}\in\text{C}$ Hence, the set of all real numbers is contained in the set of all complex numbers.
View full question & answer→Question 151 Mark
The following stetements are true? Given reason to support your answer.
Every set has a proper subset.
AnswerFalse.Explanation:
$\because$ the empty set $\oint$ has no proper subset.
View full question & answer→Question 161 Mark
Write the following statement are true? Justify your answer.
The set of all crown is contained in the set of all birds.
AnswerThe given statement is 'True'.Explanation:
$\because$ Crows are also Birds.
View full question & answer→Question 171 Mark
The following stetements are true? Given reason to support your answer.
Every subset of a finite set is finite.
AnswerTrue.Explanation:
$\because$ the order (or cardinal number) of any subset of a set is less than or equal to theorder of the set. {order (or cardinal number) of a set is the number ofelements in theset}.
View full question & answer→Question 181 Mark
Let A = {a, b, {c, d}, e}. Then the following statements is false and why?
$\text{a}\in\text{A}$
View full question & answer→Question 191 Mark
The following stetements are true? Given reason to support your answer.
{a, b, a, b, a, b, ...}
AnswerFalse.Explanation:
$\because $ {a, b, a, b,...} = {a, b} (repetition is not allowed) $\because $ {a, b, a, b,....} is a finite set.
View full question & answer→Question 201 Mark
Let $\text{A}=\{\phi,\{\phi\},1\{1,\phi\},2\}.$ Then the statement is true?
$\phi\in \text{A}.$
AnswerTrue.Explanation:
$\because\oint$ indeed belongs to A.
View full question & answer→Question 211 Mark
Let $\text{A}=\{\phi,\{\phi\},1\{1,\phi\},2\}.$ Then the statement is true?
$\{\{\phi\}\}\subset\text{A}.$
AnswerTrue.Explanation:
$\because\{\{\phi\}\}$ is a subset of A.
View full question & answer→Question 221 Mark
Let $\text{A}=\{\phi,\{\phi\},1\{1,\phi\},2\}.$ Then the statement is true?
$\{1\}\in \text{A}.$
AnswerFalse.Explanation:
$\because$ {1} is not an element of A.
View full question & answer→Question 231 Mark
The given statements is corect? Write a correct form of the given incorrect statements.$\{\text{a, b}\}\subset\{\text{a},\{\text{b, c}\}\}$
AnswerFalse.Explanation:
$\because$ {a, b} is not a subset of {a, {b, c}} The correct form is $\{\text{a, b}\}\not\subset\{\text{a},\{\text{b, c}\}\}.$
View full question & answer→Question 241 Mark
Let A = {a, b, {c, d}, e}. Then the following statements is false and why?
$\{\{\text{c, d}\}\}\subset\text{A}.$
AnswerTrue.Explanation:
$\because$ {c, d} is a subset of A.
View full question & answer→Question 251 Mark
Let A = {a, b, {c, d}, e}. Then The following statements is false and why?
$\{\text{c, d}\}\subset\text{A}$
AnswerFalse.Explanation:
{c, d} is an element of A and not a subset of A.
View full question & answer→Question 261 Mark
Write the following statement are true? Justify your answer.
The sets P = {a} and B = {{a}} are equal.
AnswerFalse.Explanation:
$\because \text{a}\in\text{P} \text{ but }\text{a}\not\in\text{B}$ Note that {a} is an element of B which is different from the element 'a'.
View full question & answer→Question 271 Mark
Let A = {{1, 2,3}, {4, 5}, {6, 7, 8}}. Then the following is true or false:
$1\in \text{A}.$
AnswerFalse.Explanation:
$\because$ 1 is not an element of A.
View full question & answer→Question 281 Mark
Let A = {{1, 2,3}, {4, 5}, {6, 7, 8}}. Then the following is true or false:
$\{\{4,5\}\}\subset\text{A}.$
AnswerTrue.Explanation:
$\because$ {{4,5}} is indeed a subset of A.
View full question & answer→Question 291 Mark
The given statements is corect? Write a correct form of the given incorrect statements.$\{\text{a}\}\subset\{\{\text{a}\},\text{b}\}$
AnswerFalse.Explanation:
$\because$ {a} is not a subset of {{a},b} hence it cannot be contained in it. The correct form is $\{\text{a}\}\in\{\{\text{a}\},\text{b}\}$ Another correct form could be $\{\{\text{a}\}\}\subset\{\{\text{a}\},\text{b}\}.$
View full question & answer→Question 301 Mark
The following stetements are true? Given reason to support your answer.
Every subset of an infinite set is infinite.
AnswerFalse.Explanation:
$\because$ {1} is a finite subset of the infinite set N of natural numbers.
View full question & answer→Question 311 Mark
Let A = {a, b, {c, d}, e}. Then The following statements is false and why?
$\{\text{c, d}\}\in\text{A}.$
AnswerTrue.Explanation:
$\because$ {c, d} is indeed an element of A.
View full question & answer→Question 321 Mark
The given statements is corect? Write a correct form of the given incorrect statements.
{x : x + 3 = 3} = $\phi$
AnswerFalse.Explanation:
$\because$ {x : x + 3 = 3} = {x : x = 0} = {0} The correct form is {x : x + 3 = 3} $\not=\oint.$
View full question & answer→Question 331 Mark
Let $\text{A}=\{\phi,\{\phi\},1\{1,\phi\},2\}.$ Then the statement is true?
$\{\phi\}\in \text{A}.$
AnswerTrue.Explanation:
$\because\oint$ is an element of A.
View full question & answer→Question 341 Mark
The given statements is corect? Write a correct form of the given incorrect statements.
$\{\text{a}\}\in \{\text{a, b, c}\}$
AnswerFalse.Explanation:
$\because$ {a} is a subset and not an element of {a, b, c} The correct form is $\{\text{a}\}\subset\{\text{a, b, c}\}.$
View full question & answer→Question 351 Mark
The given statements is corect? Write a correct form of the given incorrect statements.
$\phi\in \{\text{a, b}\}$
AnswerFalse.Explanation:
$\because\oint$ is not an element of {a, b}. The correct form is $\oint\subset\{\text{a, b}\}.$
View full question & answer→Question 361 Mark
The following stetements are true? Given reason to support your answer. A set can have infinitely many subsets.
AnswerFalse, One knows that if the cardinal number of a set $A$ is $n$, then the power set of $A$ denoted by $P(A)$ which is the set of all subsets of all, has the cardinal number $2^n$. One knows that if the cardinal number of a set $A$ is $n$, then thepower set of $A$ denoted by $P(A)$ which is the set of all subsets of all, has the cardinal number $2^n$.
View full question & answer→Question 371 Mark
Write the following statement are true? Justify your answer.
The set of all integers is contained in the set of all rational numbar.
AnswerThe given statement is 'True'.
If $\text{m}\in \text{z},$ then m can be written as $\frac{\text{m}}{1}$ which is of the form $\frac{\text{p}}{\text{q}}$ where p and q are relatively prime integers and $\text{q}\not=0$.
This implies that $\text{m}\in\text{Q}$, set of rational numbers. Thuse, $\text{m}\in\text{z}\Rightarrow\text{m}\in Q$
Hence, $\text{z}\subseteq\text{Q}.$
View full question & answer→Question 381 Mark
Let A = {{1, 2,3}, {4, 5}, {6, 7, 8}}. Then the following is true or false:
$\{6,7,8\}\in\text{A}.$
AnswerTrue.Explanation:
$\because$ {6,7,8} is indeed an element of A.
View full question & answer→Question 391 Mark
The following stetements are true? Given reason to support your answer.
For any two sets A and B aither $\text{A}\subseteq\text{B}\text{ or }\text{A}\subseteq\text{B}.$
AnswerFalse.Explanation:
$\because$ the two sets A and B need not be comparable.
View full question & answer→Question 401 Mark
Let $\text{A}=\{\phi,\{\phi\},1\{1,\phi\},2\}.$ Then the statement is true?
$\{\phi,\{\phi\},\{1,\phi\}\}\subset\text{A}.$
AnswerTrue.Explanation:
$\because\{\phi,\{\phi\},\{1,\phi\}\}$ is a subset of A.
View full question & answer→Question 411 Mark
Let $\text{A}=\{\phi,\{\phi\},1\{1,\phi\},2\}.$ Then the statement is true?
$\{2,\{1\}\not\subset\text{A}.$
AnswerTrue.Explanation:
$\because$ {2,{1}} is not a subset of A.
View full question & answer→Question 421 Mark
Let A = {a, b, {c, d}, e}. Then the following statements is false and why?
$\{\text{a, b, e}\}\in\text{A}$
AnswerFalse.Explanation:
$\because$ {a, b, e} is a subset of A. So it does not belong to A.
View full question & answer→Question 431 Mark
Let A = {{1, 2,3}, {4, 5}, {6, 7, 8}}. Then the following is true or false:
$\phi\in\text{A}.$
AnswerFalse.Explanation:
$\because\phi$ is a subset and not an element of A.
View full question & answer→Question 441 Mark
Write the following statement are true? Justify your answer.The set A = {x : x is letter of the word "LITTLE"} and, B = {x : x is a letter of the word "TITLE"} are equal.
AnswerA = {L, I, T, E} [$\because$ repetition is not allowed]
B = {T,I,L,E} [$\because$ repetition is not allowed]
= {L, I, T, E} [$\because$ the manner in which the elements are listed does not matter]
$\because$ Each element of A is an element of B and vice-versa
$\therefore$ A = B
Hence, the given statement is true.
View full question & answer→Question 451 Mark
Let A = {a, b, {c, d}, e}. Then the following statements is false and why?
$\{\phi\}\subset \text{A}$
AnswerFalse.Explanation:
$\because\oint$ and not $\{\oint\}$ is a subset of A.
View full question & answer→Question 461 Mark
Let A = {a, b, {c, d}, e}. Then the following statements is false and why?
$\{\text{a, b, c}\}\subset\text{A}$
AnswerTrue.Explanation:
$\because$ {a, b, e} is a subset of A.
View full question & answer→Question 471 Mark
State whether the following statements are true or false:
1 $\in$ {1, 2, 3}
AnswerTrue.Explanation:
$\because$ 1 is an element of the set {1, 2, 3}.
View full question & answer→Question 481 Mark
Let A = {a, b, {c, d}, e}. Then the following statements are false and why?
$\{\text{a, b, c}\}\subset\text{A}$
AnswerFalse.Explanation:
$\because$ {a, b, c} is not a subset of A.
View full question & answer→Question 491 Mark
Let $\text{A}=\{\phi,\{\phi\},1\{1,\phi\},2\}.$ Then the statement is true?
$2\subset\text{A}.$
AnswerFalse.Explanation:
$\because$ 2 is not a subset of A, it is an element of A.
View full question & answer→Question 501 Mark
qustion Decide among the following sets, which are true or false:
$A=\left\{x: x\right.$ satisfies $\left.x^2-8 x+12=0\right\}$,
$B=\{2,4,6\}$,
$C=\{2,4,6,8, \ldots\}$,
$D=\{6\}$.
Answersolution We have,
$A=\left\{x: x \text { satisfies } x^2-8 x+12=0\right\}$
$=\left\{x: x^2-6 x-2 x+12=0\right\}$
$=\{x: x(x-6)-2(x-6)=0\}$
$=\{x:(x-6)(x-2)=0\}$
$=\{x: x=6,2\}$
$=\{6,2\}$
$B=\{2,4,6\}$
$C=\{2,4,6,8, \ldots .\}$
$D=\{6\}$
We know that if E and F are two sets, then $E$ is a subset of F. i.e.,
$E \subseteq F \text { if }$
$x \in E \Rightarrow x \in F , E$ is called a proper subset of F if E is strictly contained in F and is denoted by $E \subset F$.
Clearly,
$D \subset A \{\because 6 \in D$ and $6 \in A\}$
$A \subset B \{\therefore 2,6 \in A$ and they also belong to B $\}$
Similarly, $B \subset C$
Hence, $D = A \subset B \subset C$.
View full question & answer→Question 511 Mark
Let A = {{1, 2,3}, {4, 5}, {6, 7, 8}}. Then the following is true or false:
$\phi\subset\text{A}.$
AnswerTrue.Explanation:
$\because\phi$ is a subset of every set, and hence a subset of A.
View full question & answer→Question 521 Mark
The given statements is corect? Write a correct form of the given incorrect statements.
$\text{a}\in\{\{\text{a}\}, \text{b}\}$
AnswerFalse.Explanation:
$\because$ a is not an element of {{a}, b} The correct form is $\text{a}\in\{\{\text{a}\}, \text{b}\}.$
View full question & answer→Question 531 Mark
Let A = {a, b, {c, d}, e}. Then the following statements is false and why?
$\text{a}\subset\text{A}$
AnswerFalse.Explanation:
$\because$ a belongs to A and not a subset of A. An element of a set belongs to it whereas a subset of it is contained in it.
View full question & answer→Question 541 Mark
Is it true that for any sets A and $\text{B},\text{ P(A)}\cup\text{P(B)}=\text{P(A}\cup\text{B})$? Justify your answer.
AnswerThis is a false statement
Let, A = {1} and B = {2}
Then,
$\text{P(A)}=\{\phi,\{1\}\}$
and $\text{P(A)}=\{\phi,\{2\}\}$
$\therefore\text{ P(A)}\cup\text{P(B)}=\{\phi, \{1\}, \{2\}\}$
Now,
$\text{A}\cup\text{B}=\{1, 2\}$
and $\text{P(A}\cup\text{B})=\{\phi, \{1\}, \{2\}, \{1, 2\}\}$
Hence, $\text{P(A)}\cup\text{P(B)}\not=\text{P(A}\cup\text{B).}$
View full question & answer→