Sets Test

Result

Sets Test - 29

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Weekly Quiz Competition

Question 1
1 / -0

Let $$A$$ and $$B$$ be two sets such that $$n(A)=16$$, $$n(B)=12$$, and $$n(A\cap B)=8$$. Then $$n(A\cup B)$$ equals

A
$$28$$

B
$$20$$

C
$$36$$

D
$$12$$

Solution

$$n(A\cup B)=n(A)+n(B)-n(A\cap B)=16+12-8=20$$
Question 2
1 / -0

Let $$A=\{1,2,3,4,5,6\}$$. How many subsets of $$A$$ can be formed with just two elements, one even and one odd?

A
$$6$$

B
$$8$$

C
$$9$$

D
$$10$$

Solution

$$\{1,2\}$$, $$\{1,4\}$$, $$\{1,6\}$$, $$\{2,3\}$$, $$\{2,5\}$$, $$\{3,4\}$$, $$\{3,6\}$$, $$\{4,5\}$$, $$\{5,6\}$$,
Question 3
1 / -0

In a class 60% of the students were boys and 30% of them had I class. If 50%of the students in the class had I class, find the fraction of the girls in the class who did not have a I class.

A
$$1/5$$

B
$$4/5$$

C
$$1/4$$

D
$$1/3$$

Solution

$$Let\quad the\quad number\quad of\quad students\quad be\quad x,\\ boys\quad with\quad first\quad class=0.3*0.6x=0.18x,\\ number\quad of\quad girls=0.4x,\\ students\quad with\quad first\quad class=0.5x,\\ girls\quad with\quad first\quad class=0.5x-0.18x=0.32x,\\ fraction\quad of\quad girls\quad without\quad first\quad class=\dfrac { 0.4-0.32x }{ 0.4x } =\dfrac { 1 }{ 5 } $$
Question 4
1 / -0

The sets $$\displaystyle S_{x}$$ are defined to be $$(x, x + 1, x + 2, x + 3, x + 4)$$ where $$x=1, 2, 3,.....80$$. How many of these sets contain $$6$$ or its multiple?

A
$$65$$

B
$$66$$

C
$$59$$

D
$$60$$

Solution

There are $$14$$ multiples of $$6$$ till $$84$$.

Since $$5$$ consecutive no.s are chosen only one set in $$6$$ consecutive sets will not have a multiple of $$6$$. So till $$78$$ sets there are

$$78-\dfrac{78}6=78-13=65$$ sets containing 6 or multiples of 6.

$$S_{79}$$ does not contain any multiple of 6

Hence $$S_{80} $$ must contain a multiple of 6.

Answer $$=66$$ sets
Question 5
1 / -0

If $$A=\{\dots,-6,-4,-2,0,2,4,6,\dots\}$$, then

A
$$10\notin A$$

B
$$-10\notin A$$

C
$$5\in A$$

D
$$50\in A$$

Solution

50 is even.
Question 6
1 / -0

If $$\displaystyle Q=\left((x|x=\frac{1}{y}\:\ \text{wher} \ e\:y\in N\right)$$, then

A
$$0\notin Q$$

B
$$1\in Q$$

C
$$2\in Q$$

D
$$\displaystyle\frac{2}{3}\in Q$$

Solution

When $$y=1$$, $$\displaystyle x=\frac{1}{1}=1$$.
Question 7
1 / -0

If A and B are disjoint then $$\displaystyle \left ( A\cap B \right ){}'=$$_______

A
$$A$$

B
$$B$$

C
$$\displaystyle \phi $$

D
$$\displaystyle \mu $$

Solution

When A and B are disjoint sets, they do not have any overlapping region as shown in the figure.

So, $$ (A \cap B) = \phi $$

And $$ {(A \cap B)}^{`} = \mu - \phi = \mu $$ will be the complete region of the universal set as there is no overlapping region of sets A and B
Question 8
1 / -0

If A={a,b,c,d,e}, B={a,c,e,g} and C={b,d,e,g} then which of the following is true?

A
$$\displaystyle C\subset \left ( A\cup B \right )$$

B
$$\displaystyle C\subset \left ( A\cap B \right )$$

C
$$\displaystyle A\cup B=A\cup C$$

D
Both(1) and (3)

Solution

For the given sets,
$$ (A \cup B ) = $$ { $$ a,b,c,d,e,g $$} (Combination of all elements of both sets)

Clearly, elements of C are a part of $$ A \cup B $$ as well,
So, $$ C\subset (A\cup B) $$

And, $$ (A \cap B ) = $$ { $$ a,c,e $$} (Common elements of both sets )
As the elements of C are not completely a part of $$ A \cap B $$ , Option B is not True.

Also,
$$ (A \cup C ) = $$ { $$ a,b,c,d,e,g $$}

Clearly, $$ (A \cup B ) = (A \cup C ) $$

Hence, both first option and third options are True.
Question 9
1 / -0

Three sets $$A, B, C$$ are such that $$\displaystyle A=B\cap C$$ and $$\displaystyle B=C\cap A$$, then

A
$$\displaystyle A\subset B$$

B
$$\displaystyle A\supset B$$

C
$$\displaystyle A\equiv B$$

D
$$\displaystyle A\subset { B }^{ \prime }$$

Solution

Since, $$\displaystyle A=B\cap C$$ and $$\displaystyle B=C\cap A$$, then $$\displaystyle A\equiv B$$
Question 10
1 / -0

P, Q and R are three sets and $$\xi = P\cup Q\cup R$$. Given that $$n(\xi) = 60, n (P\cap Q) = 5, n(Q\cap R) = 10, n(P) = 20$$ and $$n(Q) = 23$$, find $$n(P\cup R)$$

A
$$37$$

B
$$38$$

C
$$45$$

D
$$52$$

Solution

$$n(U) =60 (Universal \; Set) $$

$$n(P \cap Q ) = 5$$

$$n(Q \cap R ) = 10$$

$$n(P ) = 20$$

$$n(Q)=23$$

$$n(P \cup Q ) = n(P) + n(Q)- n(P \cap Q ) = 20+23-5 = 38$$

$$n(R)=n(U)-n(P \cup Q ) +n(Q\cap R)= 60-38+10 = 32$$

$$n(P \cup R ) = n(P) + n(R)- n(P \cap R ) = 20+32-0 =52$$

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Re-Attempt Weekly Quiz Competition

Sets Test - 29

Result

Sets Test - 29

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SHARING IS CARING

Question 1

$$28$$

$$20$$

$$36$$

$$12$$

Solution

Question 2

$$6$$

$$8$$

$$9$$

$$10$$

Solution

Question 3

$$1/5$$

$$4/5$$

$$1/4$$

$$1/3$$

Solution

Question 4

$$65$$

$$66$$

$$59$$

$$60$$

Solution

Question 5

$$10\notin A$$

$$-10\notin A$$

$$5\in A$$

$$50\in A$$

Solution

Question 6

$$0\notin Q$$

$$1\in Q$$

$$2\in Q$$

$$\displaystyle\frac{2}{3}\in Q$$

Solution

Question 7

$$A$$

$$B$$

$$\displaystyle \phi $$

$$\displaystyle \mu $$

Solution

Question 8

$$\displaystyle C\subset \left ( A\cup B \right )$$

$$\displaystyle C\subset \left ( A\cap B \right )$$

$$\displaystyle A\cup B=A\cup C$$

Both(1) and (3)

Solution

Question 9

$$\displaystyle A\subset B$$

$$\displaystyle A\supset B$$

$$\displaystyle A\equiv B$$

$$\displaystyle A\subset { B }^{ \prime }$$

Solution

Question 10

$$37$$

$$38$$

$$45$$

$$52$$

Solution

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