Sets Test

Result

Sets Test - 27

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Let $$P$$ and $$Q$$ be two sets then what is $$\displaystyle (P\cap Q')\cup (P\cup Q)'$$ equal to ?

A
$$\displaystyle (P\cap Q')\cup (P\cup Q)'=\xi \cap Q'=\xi \cap Q'=\xi $$

B
$$\displaystyle (P\cup Q')\cup (P\cup Q)'=\xi \cap Q'=\xi \cap Q'=\xi $$

C
$$\displaystyle (P\cap Q')\cup (P\cap Q)'=\xi \cap Q'=\xi \cap Q'=\xi $$

D
none of the above

Solution

$$\displaystyle (P\cap Q')\cup (P\cup Q)'=(P\cap Q')\cup (P'\cap Q') $$
$$=$$$$\displaystyle (P\cup P')\cap (P\cup Q')\cap (Q'\cup P')\cap (Q'\cup Q')$$
$$=$$$$\displaystyle \xi \cap \left \{ Q'\cup (P\cap P') \right \}\cap Q'$$
$$=\displaystyle \xi \cap \{Q'\cup \xi )\cap Q'$$
$$=$$$$\displaystyle \xi \cap Q'\cap Q'=\xi \cap Q'=\xi$$
Question 2
1 / -0

If $$A$$ and $$B$$ are finite sets which of the following is the correct statement?

A
$$n(A - B) = n(A) - n(B)$$

B
$$n(A - B) = n(B - A)$$

C
$$n(A - B) = n(A) -$$ $$\displaystyle n\left ( A\cap B \right )$$

D
$$n(A - B) = n(B) - $$$$\displaystyle n\left ( A\cap B \right )$$

Solution
Question 3
1 / -0

If A and B are two disjoint sets and N is universal set, then $$\displaystyle A^{\circ}\cup \left [ \left ( A\cup B \right )\cap B^{\circ} \right ]$$ is

A
$$\displaystyle \phi $$

B
$$A$$

C
$$B$$

D
$$N$$

Solution

In the Venn Diagram, we can see that $$ (A \cup B) \cap B' $$ covers the pink coloured region inside $$N$$ except $$B$$.
And $$ A' $$ is the region which is shown using striking lines , that is the region outside $$A$$
And if we perform $$ A' \cup (A \cup B) \cap B' $$, it will cover the pink region as well s the striken region, which is nothing but the complete set $$N$$.
Question 4
1 / -0

U is a universal set and n(U) = 160. A, B and C are subset of U. If n(A) = 50, n(B) = 70, $$\displaystyle n\left ( B\cup C \right )=\Phi $$, $$\displaystyle n\left ( B\cap C \right )=15 $$ and $$\displaystyle A\cup B\cup C=U $$. then n(C) equals

A
40

B
50

C
55

D
60
Question 5
1 / -0

In a town of 10000 families, it was found that 40% families buy a newspaper A, 20% families buy newspaper B and 10% families buy newspaper C. 5% families buy both A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families which buy A only.

A
$$3300$$

B
$$3500$$

C
$$3600$$

D
$$3700$$

Solution

$$n(A) = 40% of 10,000 = 4,000$$
$$n(B) = 20% of 10,000 = 2,000$$
$$n(C) = 10% of 10,000 = 1,000$$
$$n (A \cap B) = 5% of 10,000 = 500$$
$$n (B \cap C) = 3% of 10,000 = 300$$
$$n(C \cap A) = 4% of 10,000 = 400,$$
$$n(A \cap B \cap C) = 2% of 10,000 = 200$$

We want to find $$n(A\ only) = n(A) – [n(A\cap B) + n(A \cap C)] + n(A \cap B \cap C)$$

$$ n(A\ only) = 4000 – [500 + 400] + 200 = 4000 – 700 = 3300$$
Question 6
1 / -0

Suppose $$\displaystyle A_{1},A_{2},....,A_{30}$$ are thirty sets each having 5 elements and $$\displaystyle B_{1},B_{2},....,B_{n}$$ are n sets each with 3 elements. Let $$\displaystyle \bigcup_{i=1}^{30}A_{i} = \bigcup_{j=1}^{n}B_{j}=S $$ and each elements of S belongs to exactly 10 of the $$\displaystyle A_{i}$$ and exactly 9 of the $$\displaystyle B_{j}$$. Then n is equal to-

A
35

B
45

C
55

D
65

Solution

$$A_0,A_1,.............,A_{30}\implies$$ each of 5 elements
$$B_1,B_2,B_3...........n\implies$$ each of 3 elements
The number of elements in the union of the A sets is $$5(30)-r$$ where 'r' is the number repeats likewise the number of elements in the B sets $$3n-rB$$
Each element in the union (in5) is repeated 10 times in A which means if x was the real number of elements in A (not counting repeats) then q out of those 10 should be thrown away or 9x .likewise on the B side 8x of those elements should be thrown away So, $$\implies 150-9x=3n-8x$$
$$n=50-3x$$
Now in figure out what x is we need to use the fact that the union of a group of sets contains every member of each sets . If every element in 'S' is repeated 10 times that means every element in the union of the n's is repeated 10 times .
This means that $$10/10\implies 15$$ is the number of in the A's without repeats counted (same for the B's aswell ) So now
$$\cfrac{50-15}{3}=n$$
$$n=45$$
Subset:- A proper subset is nothing but it contain atleast one more element of main set .
Ex:$$\{3,4,5\}$$ is a set then the possible subsets are
$$\{3\},\{4\},\{5\},\{1,5\},\{3,4\}$$
Question 7
1 / -0

S = {1, 2, 3, 5, 8, 13, 21, 34}. Find $$\displaystyle \sum max\left ( A \right )$$ where the sum is taken over all 28 two elements subsets A to S

A
844

B
480

C
484

D
488

Solution
Question 8
1 / -0

Given n(A) = 11, n(B) = 13, n(C) = 16, $$\displaystyle n\left ( A\cap B \right )=3,n\left ( B\cap C \right )=6,n\left ( A\cap C \right )=5\: \: and\: \: n\left ( A\cap B\cap C \right )=2$$ then the value of $$\displaystyle n [ A\cup B \cup C ]=$$

A
$$24$$

B
$$27$$

C
$$25$$

D
$$28$$

Solution

We know,
$$n(A\cup B\cup C)= n(A) +n(B) +n(C)-n(A\cap B)-n(B\cap C) -n(C\cap A) + n(A\cap B \cap C)$$

$$=11+13+16-3-6-5+2=28$$
Question 9
1 / -0

In a group, if 60% of people drink tea and 70% drink coffee. What is the maximum possible percentage of people drinking either tea or coffee but not both?

A
$$100\%$$

B
$$70\%$$

C
$$30\%$$

D
$$10\%$$

Solution

To find maximum possible percentage of people drinking either coffee or tea, we can assume everyone drinks at least either of the options.

Hence

$$a+b=100$$

$$a+2b=60+70=130$$

$$b=30$$

hence $$a=70$$ which is the required area of the venn diagram.
Question 10
1 / -0

Out of 800 boys in a school 224 played cricket, 240 played hockey and 236 played basketball. Of the total 64 played both basketball and hockey, 80 played cricket and basketball and 40 played cricket and hockey, 24 players all the three games. The number of boys who did not play any game is

A
$$128$$

B
$$216$$

C
$$240$$

D
$$260$$

Solution

No. of players who played at least one game is:

By set theory

$$n(C\cup H\cup B)= n(C) +n(H) +n(B)-n(B\cap H)-n(C\cap B) -n(C\cap H) + n(C\cap H \cap B)$$

$$=224+240+236-64-80-40+24=540$$

Hence $$260$$ players do not play any game.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Sets Test - 27

Result

Sets Test - 27

Score

-

Rank

-

SHARING IS CARING

Question 1

$$\displaystyle (P\cap Q')\cup (P\cup Q)'=\xi \cap Q'=\xi \cap Q'=\xi $$

$$\displaystyle (P\cup Q')\cup (P\cup Q)'=\xi \cap Q'=\xi \cap Q'=\xi $$

$$\displaystyle (P\cap Q')\cup (P\cap Q)'=\xi \cap Q'=\xi \cap Q'=\xi $$

none of the above

Solution

Question 2

$$n(A - B) = n(A) - n(B)$$

$$n(A - B) = n(B - A)$$

$$n(A - B) = n(A) -$$ $$\displaystyle n\left ( A\cap B \right )$$

$$n(A - B) = n(B) - $$$$\displaystyle n\left ( A\cap B \right )$$

Solution

Question 3

$$\displaystyle \phi $$

$$A$$

$$B$$

$$N$$

Solution

Question 4

40

50

55

60

Question 5

$$3300$$

$$3500$$

$$3600$$

$$3700$$

Solution

Question 6

35

45

55

65

Solution

Question 7

844

480

484

488

Solution

Question 8

$$24$$

$$27$$

$$25$$

$$28$$

Solution

Question 9

$$100\%$$

$$70\%$$

$$30\%$$

$$10\%$$

Solution

Question 10

$$128$$

$$216$$

$$240$$

$$260$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.