Sets Test

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Sets Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

In a community of $$ 175$$ persons, $$40$$ read TOI, $$50$$ read the Samachar Patrika and $$100$$ do not read either. How many persons read both the papers?

A
$$16$$

B
$$17$$

C
$$15$$

D
$$14$$

Solution

Number of people who read $$TOI$$ $$n(TOI)=40$$
Number of people who read Samachar patrika, n(samachar patrika)$$=50$$
Number of people who do not read newspaper$$=100$$
Number of people who read newspaper $$(A\cup B)=$$Total number of people - people who don't read newspaper
$$=175-100=75$$
Number of persons who read both newspapers,
$$n\left( A\cap B \right) =n\left( A \right) +n\left( B \right) -n\left( A\cup B \right) $$
$$ n\left( A\cap B \right) =40+50-75$$
$$n\left( A\cap B \right) =90-75=15$$
Number of persons who read both newspapers$$=15$$
Question 2
1 / -0

If $$S$$ and $$T$$ are two sets such that $$S$$ has $$21$$ elements, $$T$$ has $$32$$ elements and $$\displaystyle S\cap T$$ has $$11$$ elements, then
find the number of elements in $$\displaystyle S\cup T$$.

A
$$47$$

B
$$42$$

C
$$37$$

D
$$52$$

Solution

Given $$n(S) = 21$$, $$n(T) = 32,$$ $$n$$($$\displaystyle S\cap T$$) $$= 11$$
Now $$n(S) + n(T) = n($$ $$\displaystyle S\cap T$$) $$+ n( $$$$\displaystyle S\cup T$$)
$$\displaystyle \Rightarrow $$ $$n($$ $$\displaystyle S\cup T$$$$) = 21 + 32 - 11 = 42 $$.
Question 3
1 / -0

In any continuous class interval table (a-b)

A
a is included

B
b is included

C
both are included

D
both are excluded

Solution

a is included b is included in the next interval
Question 4
1 / -0

Given $$P(A \cup B)=0.6, P(A\cap B)=0.2$$, the probability of exactly one of the event occurs is

A
$$0.4$$

B
$$0.2$$

C
$$0.6$$

D
$$0.8$$

Solution

Given, $$P(A\cup B)=0.6, P(A\cap B)=0.2$$
Probability of exactly one of the event occurs is $$P(\bar{A}\cap B)+P(A\cap \bar{B})$$
$$=P(B)-P(A\cap B)+P(A)-P(A\cap B)$$
$$=P(A\cup B)+P(A\cap B)-2P(A\cap B)$$
$$[\because P(A\cup B)=P(A)+P(B)-P(A\cap B)]$$
$$=P(A\cup B)-P(A\cap B)$$
$$=0.6-0.2$$
$$=0.4$$
Question 5
1 / -0

Directions For Questions

$$\mu = \left \{a, b, c, d, e, f, g, h, i, j\right \}$$
$$P = \left \{a, b, c, e\right \}$$
$$Q = \left \{b, c, d, f\right \}$$ and
$$R = \left \{c, f, h, i, j\right \}$$
Find the number of elements of the set

...view full instructions

$$P\cap Q\cup R$$

A
$$\left \{b, c, d, h, i, j\right \}$$

B
$$\left \{b, c, d, g, i, j\right \}$$

C
$$\left \{b, c, f, h, i, j\right \}$$

D
$$\left \{b, c, f, g, i, j\right \}$$

Solution

$$ P = \left \{ a,b,c,e \right \} $$
$$ Q = \left \{ b,c,d,f \right \} $$
$$ \Rightarrow (P\cap Q) = \left \{ b,c \right \} $$
As $$ R = \left \{ c,f,h,i,j\right \} $$
$$ \Rightarrow \boxed {(P\cap Q)\cup R = \left \{ b,f,h,i,j \right \}} $$
Question 6
1 / -0

If $$A, B$$ and $$C$$ are any three set, then $$A \cup (B\cap C) =$$

A
$$ (A \cup B) \cup (A\cup C)$$

B
$$ (A \cup B) \cap (A\cup C)$$

C
$$ (A \cap B) \cap (A\cap C)$$

D
none

Solution

Using distributive law of sets option B is correct
Or it is the distributive law itself
Question 7
1 / -0

Directions For Questions

$$\mu = \left \{a, b, c, d, e, f, g, h, i, j\right \}$$
$$P = \left \{a, b, c, e\right \}$$
$$Q = \left \{b, c, d, f\right \}$$ and
$$R = \left \{c, f, h, i, j\right \}$$
Find the number of elements of the set

...view full instructions

$$(P\cap Q)\cup (Q\cap R)$$

A
$$\left \{b, c, f\right \}$$

B
$$\left \{b, c, d\right \}$$

C
$$\left \{b, c, d, f\right \}$$

D
$$\left \{b, c, f, g\right \}$$

Solution

$$ P = \left \{ a,b,c,e \right \};Q = \left \{ b_{n}c_{n}d_{n}f \right \} $$
$$ \Rightarrow (P\cap Q) = \left \{ b,c \right \} $$
As $$ R = \left \{ c,f,n,i,j \right \} \Rightarrow (Q\cap R) = \left \{ c,f \right \} $$
$$ \boxed { (P\cap Q)\cup (Q\cap R) = \left \{ b,c,f \right \}} $$
Question 8
1 / -0

In a school with an envolment of $$950$$ students, each student must join either the lions club or the country club or both. Given that $$646$$ students are members of the lions club and $$532$$ are members of the country club, calculate the number of students who are members of both clubs

A
$$228$$

B
$$230$$

C
$$232$$

D
$$234$$

Solution

Total number of students $$=950$$
Number of students who are members of lion club $$=646$$
Number of students who are members of country club $$=532$$
Number of students who are members of both club $$=(646+532)-950$$
$$=1178-950$$
$$=228$$
$$\therefore$$ There are $$228$$ students who joined both clubs.
Question 9
1 / -0

Directions For Questions

If $$A = \left \{2, 3, 4, 5\right \}, B = \left \{1, 3, 4, 5, 6\right \}, C = \left \{1, 3, 4, 5, 7, 8\right \}$$ and $$\cup = \left \{1, 2, 3, 4, 5, 6, 7, 8\right \}$$, then find

...view full instructions

$$A - (B\cup C)$$

A
$$\left \{1,6,7,8\right \}$$

B
$$\left \{3,4,5\right \}$$

C
$$\left \{2\right \}$$

D
none

Solution

$$ (B\cup C) = \left \{ 1,3,4,5,6,7,8 \right \} $$
$$ \therefore A - (B\cup C) = \left \{ 2 \right \}\begin{bmatrix} \because 3,4,5\,are\\present\,in\,B\cup C \end{bmatrix}$$
Question 10
1 / -0

If A and B be two sets containing $$4$$ and $$8$$ elements respectively, what can be the maximum number of elements in $$A\cup B$$? Find also, the minimum number of elements in $$(A\cup B)$$?

A
Maximum number of elements $$= 12$$
Minimum number of elements $$= 8$$

B
Maximum number of elements $$= 14$$
Minimum number of elements $$= 8$$

C
Maximum number of elements $$= 12$$
Minimum number of elements $$= 9$$

D
Maximum number of elements $$= 14$$
Minimum number of elements $$= 7$$

Solution

$${\textbf{Step -1: Find maximum number of elements.}}$$
$${\text{Given,}}$$
$$n(A) =4$$
$$n(B) =8$$
$${\text{Minimum number of elements in}}$$ $$A\cup B=8.$$
$${\text{A is subset of B.}}$$
$${\text{Maximum number of elements in}}$$ $$A\cup B=4+8=12.$$
$${\textbf{[All element taken in both set A and B and elements in both sets are different.]}}$$
$${\textbf{Hence , maximum number of elements in}}$$ $$\mathbf{(A \cup B) =12.}$$

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Re-Attempt Weekly Quiz Competition

Sets Test - 16

Result

Sets Test - 16

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SHARING IS CARING

Question 1

$$16$$

$$17$$

$$15$$

$$14$$

Solution

Question 2

$$47$$

$$42$$

$$37$$

$$52$$

Solution

Question 3

a is included

b is included

both are included

both are excluded

Solution

Question 4

$$0.4$$

$$0.2$$

$$0.6$$

$$0.8$$

Solution

Question 5

$$\left \{b, c, d, h, i, j\right \}$$

$$\left \{b, c, d, g, i, j\right \}$$

$$\left \{b, c, f, h, i, j\right \}$$

$$\left \{b, c, f, g, i, j\right \}$$

Solution

Question 6

$$ (A \cup B) \cup (A\cup C)$$

$$ (A \cup B) \cap (A\cup C)$$

$$ (A \cap B) \cap (A\cap C)$$

none

Solution

Question 7

$$\left \{b, c, f\right \}$$

$$\left \{b, c, d\right \}$$

$$\left \{b, c, d, f\right \}$$

$$\left \{b, c, f, g\right \}$$

Solution

Question 8

$$228$$

$$230$$

$$232$$

$$234$$

Solution

Question 9

$$\left \{1,6,7,8\right \}$$

$$\left \{3,4,5\right \}$$

$$\left \{2\right \}$$

none

Solution

Question 10

Maximum number of elements $$= 12$$Minimum number of elements $$= 8$$

Maximum number of elements $$= 14$$Minimum number of elements $$= 8$$

Maximum number of elements $$= 12$$Minimum number of elements $$= 9$$

Maximum number of elements $$= 14$$Minimum number of elements $$= 7$$

Solution

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Maximum number of elements $$= 12$$
Minimum number of elements $$= 8$$

Maximum number of elements $$= 14$$
Minimum number of elements $$= 8$$

Maximum number of elements $$= 12$$
Minimum number of elements $$= 9$$

Maximum number of elements $$= 14$$
Minimum number of elements $$= 7$$