Set Theory Test 3

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Set Theory Test 3

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Weekly Quiz Competition

Question 1
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Let $$A$$ $$=$$ set of all cuboids and B $$=$$ set of all cubes. Which of the following is true?

A
$$A\subset B$$

B
$$B\subset A$$

C
$$B=A$$

D
$$B\in A$$

Solution

Cube is a special cuboid.
Question 2
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In Question some relationship have been expressed through symbols as defined below : (N-83)
+ - x $$\displaystyle\div $$ = > <
V $$\displaystyle\Lambda $$ ( ) U $$\displaystyle\cap $$ 0
In question only one of the five relationship is correct Find the correct one and encircle its serial number on the space provided against the question ______________.

A
24 $$\displaystyle\cap $$ 3 ( 4 V 2 ) 8

B
24 U 3 V 4 $$\displaystyle\Lambda $$ 2 ) 8

C
24 ( 3 0 4 ) 2 V 8

D
24 0 3 ( 4 $$\displaystyle\Lambda $$ 2 V 8

E
24 $$\displaystyle\Lambda $$ 3 V 4 U 2 ( 8

Solution

Answer (a) becomes-
24 > 3 x 4 + 2 ÷ 8
24 > 12 + 14 is correct
Question 3
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Set $$A$$ has $$3$$ elements and set $$B$$ has $$6$$ elements. What can be the minimum number of elements in $$A\cup B$$?

A
$$6$$

B
$$3$$

C
$$9$$

D
$$18$$

Solution

$$A\cup B$$ must contain all the elements of the bigger set B.
Question 4
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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 5
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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 6
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M represents the children in a class who have no brothers and 8 represents the children who have no sisters. $$+$$ denotes union, $$*$$ denotes intersection, and $$(^\prime)$$ denotes complement. The set of children who have no siblings is

A
$$S^\prime+M^\prime$$

B
$$(S*M)^\prime$$

C
$$(S+M)^\prime$$

D
$$S*M$$

Solution

Solution
As per De Morgan's Law,
$$\acute { \left( A\cup B \right) } =\acute { A } \cap \acute { B } $$.
Correct answer is C, that is Set of children having no children.
Question 7
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Which of the following sets is finite?

A
$$\{x:x\:is\:an\:odd\:number\}$$

B
$$\{x:3 < x < 6,x\in R\}$$

C
Set of all prime numbers

D
Set of all sand particles on earth

Solution

The correct answer is B

A set is said to be a finite set, if it is either void set or the process of counting of elements surely comes to an end is called a finite set.

and in only case B the range is defined, and rest of them ranges are not defined.
Question 8
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Which of the following has only one subset?

A
$$\{0,1\}$$

B
$$\{1\}$$

C
$$\{0\}$$

D
$$\{\}$$

Solution

Empty set is the subset of itself.
Question 9
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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 10
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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

$$(A\cup B)'$$

A
$$\left \{1,2,3,4,5,6\right \}$$

B
$$\left \{7,8\right \}$$

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

D
none

Solution

$$ (A\cup B) = \left \{ 1,2,3,4,5,6 \right \} $$
$$ \therefore (A\cup B)^{1} = \cup -(A\cup B) = \left \{ 7,8 \right \} $$

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Set Theory Test 3

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Set Theory Test 3

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Question 1

$$A\subset B$$

$$B\subset A$$

$$B=A$$

$$B\in A$$

Solution

Question 2

24 $$\displaystyle\cap $$ 3 ( 4 V 2 ) 8

24 U 3 V 4 $$\displaystyle\Lambda $$ 2 ) 8

24 ( 3 0 4 ) 2 V 8

24 0 3 ( 4 $$\displaystyle\Lambda $$ 2 V 8

24 $$\displaystyle\Lambda $$ 3 V 4 U 2 ( 8

Solution

Question 3

$$6$$

$$3$$

$$9$$

$$18$$

Solution

Question 4

$$47$$

$$42$$

$$37$$

$$52$$

Solution

Question 5

a is included

b is included

both are included

both are excluded

Solution

Question 6

$$S^\prime+M^\prime$$

$$(S*M)^\prime$$

$$(S+M)^\prime$$

$$S*M$$

Solution

Question 7

$$\{x:x\:is\:an\:odd\:number\}$$

$$\{x:3 < x < 6,x\in R\}$$

Set of all prime numbers

Set of all sand particles on earth

Solution

Question 8

$$\{0,1\}$$

$$\{1\}$$

$$\{0\}$$

$$\{\}$$

Solution

Question 9

$$16$$

$$17$$

$$15$$

$$14$$

Solution

Question 10

$$\left \{1,2,3,4,5,6\right \}$$

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

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

none

Solution

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