Sets, Relations and Functions Test

Result

Sets, Relations and Functions Test - 42

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
4 / -1

Let A = {(x,y) : y = e^x , x ϵ R}, B = {(x,y) : y = e^-x , x ϵ R} then

A
A ∩ B = ϕ

B
A ∩ B = ϕ

C
A ∪ B = R

D
A ∪ B = A

Solution
Question 2
4 / -1

Let R be a relation in N defined by R={(1 + x, 1 + x² ) / x < 5, x ϵ N} which of the following is false ?

A
R = {(2,2), (3,5), (4,10), (5,17), (6,25)}

B
Domain of R = {2,3,4,5,6}

C
Range of R = {2,5,10,17,26}

D
(2) and (3) are true
Question 3
4 / -1

The relation ≤ on numbers has the following properties.
(i) a ≤ a ∀ a ϵ R (Reflexivity)
(ii) If a ≤ b and b ≤ a then a = b ∀ a, b ϵ R (Antisymmetry)
(iii) If a ≤ b and b ≤ c then a ≤ c ∀ a, b ϵ R (Transitivity)
Which of the above properties the relation ⊂ on p(A) has ?

A
(i) and (ii)

B
(i) and (iii)

C
(ii) and (iii)

D
(i), (ii) and (iii)

Solution
Question 4
4 / -1

A Relation R is defined in the set of integers I as follows (x,y) ϵ R if x 2+ y² = 9 which of the following is false ?

A
R = {(0,3), (0,-3), (3,0), (-3,0)}

B
Domain of R = {-3,0,3}

C
Range of R = {-3,0,3}

D
None of the above

Solution
Question 5
4 / -1

Let R be the real line consider the following subsets of the plane R × R ,S = {(x, y) / y = x + 1 and 0 < x < 2}, T = {(x, y) / x - y is an integer}.Which one of the following is true ?

A
T is an equivalence relation on R but S is not.

B
Neither S nor T is an equivalance relation on R

C
Both S and T are equivalence relations on R

D
S is an equivalence relation on R but T is not.

Solution
Question 6
4 / -1

Let W denotes the words in the English dictionary Define the relation R by R = {(x, y) ϵ W × W the ward x and y have at least one letter in comman} Then R is

A
Not reflexive, symmetric and transitive

B
Reflexive, symmetric and not transitive

C
Reflexive, symmetric and transitive

D
Reflexive, not symmetric and transitive

Solution
Question 7
4 / -1

Which one of the following relations on R is an equivalence relation ?

A

B

C

D

Solution
Question 8
4 / -1

Which of the following defined on Z is not an equivalence relation.

A

B

C

D

Solution
Question 9
4 / -1

A
S₁ is not a graph of a function

B
S₂ is not a graph of a functicn

C
S₃ is not a graph of a function

D
S₄₁ is not a graph of a function

Solution
Question 10
4 / -1

The relation R defined on the let A = {1,2,3,4,5} by R = {(x, y) / | x² - y² | < 16} is given by

A
{(1,1), (2,1), (3,1), (4,1), (2,3)}

B
{(2,2), (3,2), (4,2), (2,4)}

C
{(3,3), (4,3), (5,4), (3,4)}

D
None of these