Hexaware Sets, Theory and Functions Quiz 1

Answer: A
Explanation Let the number of tasks be x.
If every interns work one task daily, the number of interns would be x (60) = 60x
Since every interns works 5 tasks, the number of interns = [x * 60] / [5] = 300
x = 25

Function f: R → R is defined by f (x) = ex.
Let x1, x2 ∈ R and f (x1) = f (x2) or ex1 = ex2 or x1 = x2.
Therefore, f is one-one.
Let f (x) = ex = y.
Taking log on both sides, we get x = logy.
We are aware that zero is not any real number's preimage, the function is not onto, and negative real numbers do not have pre-images.
Therefore, function f is into.

Explanation,

M-N = N-M is two sets that will only satisfy if M and N are equal.

Answer: 76
Given U= 240 players
10% of 240= 24 players
Hence the total number of players who could play only rugby or Only cricket.
= 240- (60+80+24)= 240-164= 76

Answer: 18

Explanation:

Let the students who selected Spanish be ‘S’ and students who chose Chinese be ‘C.’

Therefore number of students who selected at least 1 subject= n(S∪C)

Given

Each student selected at least 1 subject

Therefore n(S∪C)= 40

n(S∪C)= n(S) + n(C) – n(S∩C) = 40= n(S)+ 22- 12

n(S)= 30 (Students who selected Spanish plus both the subjects)

But since we’ve to find students who selected only Spanish

Therefore n(Only Spanish)= n only Spanish - n(S∩C)= 30-12= 18

Answer: 58%

Percentage of audience who like to read both DC movies and Marvel Movies  = 70+90- 100= 60%

The proportion of audience who like to have DC movies, Marvel Movies , and disney movies= 60+98-100= 58%

Answer: C,D,E are the subsets of UNO cards
Explanation:
we can see that C, D and E have the terms which are there in ∪. Therefore, C, D and E are the subsets of UNO cards.

Explanation:
It is given that A = {1, 2, 3}, B = {4, 5, 6, 7}.
f: A → B is defined as f = {(1, 4), (2, 5), (3, 6)}.
∴ f (1) = 4, f (2) = 5, f (3) = 6
It is seen that the images of distinct elements of A under f are distinct.
Hence, function f is one-one.

Explanation:
R = {(T1, T2): T1 is similar to T2}
R is reflexive since every triangle is similar to itself.
Further, if (T1, T2) ∈ R, then T1 is similar to T2.
⇒ T2 is similar to T1.
⇒ (T2, T1) ∈R
∴R is symmetric.
Let (T1, T2), (T2, T3) ∈ R.
⇒ T1 is similar to T2 and T2 is similar to T3.
⇒ T1 is similar to T3.
⇒ (T1, T3) ∈ R
∴ R is transitive.
Thus, R is an equivalence relation.
Now, we can observe that:



The corresponding sides of triangles T1 and T3 are in the same ratio.
Then, triangle T1 is similar to triangle T3.
Hence, T1 is related to T3.

Students who preferred I-Phone= n(P)
Students who preferred Android= n(A)
Therefore n(P∩A) Students who could prefer both.
Thus using the formula n(PUA) = n(P) + n(A) – n(P∩A)
n(PUQ) = 80 + 60 – 20= 120