Set Theory Test 6

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Set Theory Test 6

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Weekly Quiz Competition

Question 1
1 / -0

How many rural uneducated people are employed?

A
$$10$$

B
$$6$$

C
$$12$$

D
$$14$$

Solution

Rural uneducated people has been represented by $$'10'$$.
Question 2
1 / -0

If $$A=\left\{ 2,4\left\{ 5,6 \right\} ,8 \right\} $$, then which one of the following statements is not correct?

A
$$\left\{ 5,6 \right\} \subseteq A$$

B
$$\left\{ 5,6 \right\} \in A$$

C
$$\left\{ 2,4,8 \right\} \subseteq A$$

D
$$2,4,8\in A\quad $$

Solution

$$\left\{ 5,6 \right\} $$ is not the subset but is an element of $$A$$, $$\therefore$$ a is false.
Question 3
1 / -0

Upper limit of class $$'41 - 50'$$ is __________.

A
$$41$$

B
$$50$$

C
$$45$$

D
$$91$$

Solution

Upper Limit of class $$'41-50'=50$$
Part (B) is correct answer.
Question 4
1 / -0

If $$A=\left\{a,b,c\right\},B=\left\{c,d,e\right\},C\left\{a,d,f\right\},$$ then $$A\times \left( B\cup C \right)$$ is

A
$$\left\{(a,d),(a,e),(a,c)\right\}$$

B
$$\left\{(a,d),(b,d),(c,d)\right\}$$

C
$$\left\{(d,a),(d,b),(d,c)\right\}$$

D
$$none\ of\ these$$

Solution

$$(d)$$.
$$A\times \left( B\cup C \right) =\{ a,b,c\} \times \{ a,c,d,e,f\}$$
The above set will consist of $$15$$ ordered pairs and not $$3$$.
Question 5
1 / -0

$$A$$ and $$B$$ are two sets having $$3$$ and $$5$$ elements respectively and having $$2$$ elements in common. Then the number of elements in $$A\times B$$ is

A
$$6$$

B
$$36$$

C
$$15$$

D
$$None\ of\ these$$

Solution

Total ordered pairs $$= n(A) \times n(B) = 3\times 5 = 15$$
Question 6
1 / -0

Let $$A$$ and $$B$$ have $$3$$ and $$6$$ elements respectively. What can be the minimum number of elements in $$A\cup B$$?

A
$$3$$

B
$$6$$

C
$$9$$

D
$$18$$

Solution

Ans. $$(b)$$.
$$n\left( A\cup B \right) =n(A)+n(B)-n\left( A\cap B \right)$$
Now $$A$$ has $$3$$ elements and $$B$$ has $$6$$ elements. If they are disjoint, then $$n\left( A\cap B \right) =0$$.
$$\therefore n\left( A\cup B \right) =6+3=9$$
If $$A\subset B$$ then $$A\cup B=B$$
$$\therefore \left( A\cup B \right) =n(B)=6$$
$$B$$ cannot be a subset of $$A$$ and hence the other possibility of $$A\cup B=A$$ is ruled out.
Question 7
1 / -0

For two sets $$A$$ and $$B$$, $$ A\cap \left( A\cup B \right)=$$

A
$$A$$

B
$$B$$

C
$$ \phi$$

D
$$None\ of\ these$$

Solution

$$\left( A\cap A \right) \cup \left( A\cap B \right) =A\cup \left( A\cap B \right) =A$$
$$\because A\cap B\subset A$$
Question 8
1 / -0

$$25$$ people for applied for programme $$A$$, $$50$$ people for programme $$B$$, $$10$$ people for both. So number of employee applied only for $$A$$ is

A
$$15$$

B
$$20$$

C
$$35$$

D
$$40$$

Solution

$$n(A - B) = n(A) - n(A \cap B) = 25 -10 -15$$
Question 9
1 / -0

If $$P(A) = 0.8 , P(B) = 0.5 $$ & $$P(B/A) =0.4 $$ find (i) $$P(A \cap B) $$ (ii) $$P(A/B)$$ (iii) $$P(A\cup B)$$.

A
$$i) 0.32, ii)0.64 , iii)0.98$$

B
$$i) 0.62, ii)0.34 , iii)0.88$$

C
$$i) 0.66, ii)0.32 , iii)0.98$$

D
none

Solution

$$\\\>P(\frac{B}{A})=\>\frac{P(B\>\cap\>A)}{P(A)}\\\>0.4=\frac{P(B\cap\>A)}{0.8}\\$$
$$\therefore\>P(B\cap\>A)=0.32\\$$, $$\implies \>P(A\cap\>B)=0.32\\$$
$$then\>\>P(\frac{A}{B})=\>\frac{P(A\>\cap\>B)}{P(B)}=(\frac{0.32}{0.5})=0.64\>\\$$
$$and\>P(A\cup\>B)=P(A)+P(B)-P(A\cap\>B)\\=0.8+0.5-0.32\\\>=0.98$$
Question 10
1 / -0

Let $$A$$ is a finite set such that $$n(A)=6$$ then $$n[P(A)]$$ is

A
$$32$$

B
$$36$$

C
$$63$$

D
$$64$$

Solution

We have if a set contains $$n$$ element then its power set contains $$2^n$$ elements.
In our problem $$n=6$$.
Then $$n[P(A)]=2^6=64$$.

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Re-Attempt Weekly Quiz Competition

Set Theory Test 6

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Set Theory Test 6

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SHARING IS CARING

Question 1

$$10$$

$$6$$

$$12$$

$$14$$

Solution

Question 2

$$\left\{ 5,6 \right\} \subseteq A$$

$$\left\{ 5,6 \right\} \in A$$

$$\left\{ 2,4,8 \right\} \subseteq A$$

$$2,4,8\in A\quad $$

Solution

Question 3

$$41$$

$$50$$

$$45$$

$$91$$

Solution

Question 4

$$\left\{(a,d),(a,e),(a,c)\right\}$$

$$\left\{(a,d),(b,d),(c,d)\right\}$$

$$\left\{(d,a),(d,b),(d,c)\right\}$$

$$none\ of\ these$$

Solution

Question 5

$$6$$

$$36$$

$$15$$

$$None\ of\ these$$

Solution

Question 6

$$3$$

$$6$$

$$9$$

$$18$$

Solution

Question 7

$$A$$

$$B$$

$$ \phi$$

$$None\ of\ these$$

Solution

Question 8

$$15$$

$$20$$

$$35$$

$$40$$

Solution

Question 9

$$i) 0.32, ii)0.64 , iii)0.98$$

$$i) 0.62, ii)0.34 , iii)0.88$$

$$i) 0.66, ii)0.32 , iii)0.98$$

none

Solution

Question 10

$$32$$

$$36$$

$$63$$

$$64$$

Solution

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