Sets Test

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Sets Test - 40

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Weekly Quiz Competition

Question 1
1 / -0

In a universal set x,$$n\left( x \right) = 50$$ ,$$n\left( A \right) = 35$$ , $$n\left( B \right) = 20$$ , $$n\left( {A' \cap B'} \right) = 5$$ ,then $$n\left( {A \cup B} \right),n\left( {A \cap B} \right)$$ are repsectively

A
$$45,10$$

B
$$10,45$$

C
$$25,30$$

D
$$15,25$$

Solution

Given $$n\left(X\right) = 50$$,
$$n\left(A\right) = 35$$,
$$n\left(B\right) = 20$$
$$n\left({A}^{\prime}\cap\,{B}^{\prime}\right) = 5$$

$$(i)\,n\left(A \cup B\right)$$
$$n\left({A}^{\prime}\cap\,{B}^{\prime}\right) = n\left(X\right) - n\left(A\cup\,B\right)$$
$$n\left(A\cup\, B\right) = n\left(X\right) - n\left({A}^{\prime}\cap\,{B}^{\prime}\right)$$
$$n\left(A\cup\, B\right) = 50 - 5= 45$$

$$(ii) n\left(A \cap B\right)$$
$$n\left(A\cup B\right) = n\left(A\right) + n\left(B\right) - n\left(A\cap B\right)$$
$$n\left(A\cap\, B\right) = n\left(A\right) + n\left(B\right) - n\left(A\cup\, B\right)$$
$$n\left(A\cap\, B\right) = 35 + 20 - 45= 10$$
Question 2
1 / -0

If $$A$$ and $$B$$ are two non empty sets then $$( A \cup B ) ^ { C } = ?$$

A
$$A ^ { C } \cup B ^ { C }$$

B
$$A ^ { C } \cap B ^ { C }$$

C
$$A \cup B ^ { C }$$

D
$$A ^ { C } \cap B$$

Solution

If A and B are two no empty sets then $${ \left( A\cup B \right) }^{ C }={ A }^{ C }\cap { B }^{ C }$$
Question 3
1 / -0

Let $$S={1,2,3,.....10}$$ and $$P={1,2,3,4,5}$$ The number of subsets $$'Q'$$ of $$S$$ such that $$p \cup Q=S$$, are.....

A
$$128$$

B
$$256$$

C
$$32$$

D
$$64$$
Question 4
1 / -0

The statement that is true among the following is

A
$$p\Longrightarrow q$$ is equivalent to $$p\wedge -q$$

B
$$p\vee q$$ and $$p\wedge q$$ have the same truth value

C
The converse of $$tanx=0\Longrightarrow x=0$$ is $$x\neq 0\Longrightarrow tanx=0$$

D
The contrapositive of $$3x+2=8\Longrightarrow x=2$$ is $$x\neq 2\Longrightarrow 3x+2\neq 8$$

Solution
Question 5
1 / -0

Let $$Q$$ be a non empty subset of $$N$$ and $$q$$ is a statement as given below :
$$q:$$ There exists an even number $$a \in Q$$ Negation of the statement $$q$$ will be :

A
There is no even number in the set $$Q$$

B
Every $$a \in Q$$ is an odd number.

C
$$(a)$$ and $$(b)$$ both

D
None of these

Solution

Let $$Q$$ be a non empty subset of $$N$$ and $$q.$$ There exists even number $$a\in Q$$ negation of statement $$q.$$ There does not exist a even number in set Q.
Hence, the answer is there is no even number in the set $$Q.$$
Question 6
1 / -0

In a battle $$70$$% of the combatants lost one eye, $$80$$% an ear, $$75$$% an arm, $$85$$% a leg, $$x$$% lost all the four limbs the minimum value of $$x$$ is

A
$$10$$

B
$$12$$

C
$$15$$

D
$$5$$

Solution

$$70\%$$ of the combatants lost one eye, $$80\%$$ an ear, $$75\%$$ an arm and $$85\%$$ a leg.
Now,
$$\Rightarrow$$ The combatants who lost one eye and one ear $$=(70+80-100)\%$$
$$=50\%$$

$$\Rightarrow$$ The combatants who lost one eye, one ear and one erm $$=(50+75-100)\%$$
$$=25\%$$

$$\Rightarrow$$ The combatants who lost one eye, one ear one arm and one leg $$=(25-85-100)\%$$
$$=10\%$$
$$\therefore$$ Combatant who lost all the four limbs $$=10\%$$
$$\therefore$$ $$x=10\%$$
Question 7
1 / -0

The value of set $$(A\cup B\cup C)\cap(A\cap B^1\cap C^1)^1\cap C^1$$ is equal to

A
$$B\cap C^1$$

B
$$A\cap C$$

C
$$B\cap C^1$$

D
$$A\cap C^1$$

Solution
Question 8
1 / -0

Two sets A and B are defined as follows
$$A=\left\{ \left( x,y \right) :y={ e }^{ 2x },x\in R \right\} $$ and
$$B=\left\{ \left( x,y \right) :y={ x }^{ 2 },x\in R \right\} $$, then

A
$$A\subset B$$

B
$$B\subset A$$

C
$$A\bigcup B$$

D
$$A\cap B=\phi $$

Solution

$$\begin{array}{l} A=\left\{ { \left( { x,\, y } \right) \, :\, y={ e^{ 2x } },\, x\in R } \right\} \, and \\ B=\left\{ { \left( { x,\, y } \right) \, :\, y={ x^{ 2 } },\, x\in R } \right\} \\ then, \\ A=\left( { { e^{ \circ } },\, { e^{ 1 } },\, { e^{ 2 } },....,\, { e^{ \infty } } } \right) \\ =\left( { 1,\, { e^{ 1 } },\, { e^{ 2 } },....... } \right) \\ and, \\ B=\left( { 0,\, 1,\, 4,\, ..... } \right) \\ \therefore A\subset B \\ Hence,\, the\, option\, A\, is\, the\, correct\, answer. \end{array}$$
Question 9
1 / -0

If two sets $$P$$ and $$Q,n\left(P\right)=5,n\left(Q\right)=4$$ then $$n\left(P\times Q\right)=$$

A
$$20$$

B
$$9$$

C
$$25$$

D
$$5/4$$

Solution

$$\begin{aligned} n(P \times Q) &=n(P) \times n(Q) \\ &=5 \times 4 \\ &=20 \end{aligned}$$
$$\therefore$$ option $$A$$ is correct.
Question 10
1 / -0

If A= {1, 2, 5} and B= {3, 4, 5, 9}, then $$A \bigcup B$$ is equal to :

A
$$\{1, 2, 5, 9\}$$

B
$$\{1, 2, 3, 4, 9\}$$

C
$$\{1, 2, 3, 4, 5, 9\}$$

D
None of these

Solution

$$A=\left\{ 1,2,5 \right\} \quad B=\left\{ 3,4,5,9 \right\} $$
$$A\cup B=\left\{ 1,2,3,4,5,9 \right\} $$
Option C.

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Re-Attempt Weekly Quiz Competition

Sets Test - 40

Result

Sets Test - 40

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SHARING IS CARING

Question 1

$$45,10$$

$$10,45$$

$$25,30$$

$$15,25$$

Solution

Question 2

$$A ^ { C } \cup B ^ { C }$$

$$A ^ { C } \cap B ^ { C }$$

$$A \cup B ^ { C }$$

$$A ^ { C } \cap B$$

Solution

Question 3

$$128$$

$$256$$

$$32$$

$$64$$

Question 4

$$p\Longrightarrow q$$ is equivalent to $$p\wedge -q$$

$$p\vee q$$ and $$p\wedge q$$ have the same truth value

The converse of $$tanx=0\Longrightarrow x=0$$ is $$x\neq 0\Longrightarrow tanx=0$$

The contrapositive of $$3x+2=8\Longrightarrow x=2$$ is $$x\neq 2\Longrightarrow 3x+2\neq 8$$

Solution

Question 5

There is no even number in the set $$Q$$

Every $$a \in Q$$ is an odd number.

$$(a)$$ and $$(b)$$ both

None of these

Solution

Question 6

$$10$$

$$12$$

$$15$$

$$5$$

Solution

Question 7

$$B\cap C^1$$

$$A\cap C$$

$$B\cap C^1$$

$$A\cap C^1$$

Solution

Question 8

$$A\subset B$$

$$B\subset A$$

$$A\bigcup B$$

$$A\cap B=\phi $$

Solution

Question 9

$$20$$

$$9$$

$$25$$

$$5/4$$

Solution

Question 10

$$\{1, 2, 5, 9\}$$

$$\{1, 2, 3, 4, 9\}$$

$$\{1, 2, 3, 4, 5, 9\}$$

None of these

Solution

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