MTH202 Quiz 1 by VU Topper RM

Domain of the relation {(0,1),(3,22),(90,34)}is ___________ . A. {1,22,34} B. {0,1,3} C. {0,1,3,22,90,34} D.

{0,3,90}

Let P(A) be the power set of a non-empty set A and by using the definition of “subset” relation, ⊆, for all X, Y ∈ P(A), X ⊆ Y ⇔ ∀ x, iff x ∈X then x ∈Y. Then _______. A. ⊆ is a partial order relation. B. ⊆ is not a partial order relation.

Let R be the universal relation on a set A then which one of the following statement about R is true?

A. R is not reflexive B. R is not transitive C. R is reflexive, symmetric and transitive. D. R is not symmetric

Let A={1 , 2 , 3 , 4} and R={(1 , 1)(2 , 2)(3 , 3)(4 , 4)} then R is A. Symmetric B. Options a,b,and c all true C.

Reflexive

D.

R={(a,1)(b,2)(c,3)(d,4)} then the inverse of this relation is............. A. {(a,1)(2,b)(3,c)(4,d)} B.

{(1,a)(2,b)(3,c)(4,d)}

C. {(a,1)(b,2)(3,c)(4,d)} D. {(1,a)(b,2)(3,c)(4,d)}

Range of the relation {(0,1),(3,22),(90,34)}is ___________ . A. {0,3,90} B. {0,1,3,22,90,34} C.

{1,22,34}

D. {0,1,3}

Let A = {1,2,3} and R be the relation defined on A such that R ={(1,1), (1,2), (2,3), (3,1)}, then R is _______ . A. Symmetric B.

Let R and S be transitive relations on a set A then __________________

A. Both R union S and R intersection S are transitive B.

R intersection S is transitive

C. Neither R union S is transitive nor R intersection S is transitive D. R union S is transitive

There is atleast one loop in the graph of an irreflexive relation. A. true B.

false

Let R be a binary relation on a set A.R is anti-symmetric iff ________. A. a, b ∈A if (a,b) ∈R and (b,a) ∈R then a = b B.

a, b ∈A if (a,b) ∈R and (b,a) ∈R then a ≠ b

C. a, b ∉A if (a,b) ∈R and (b,a) ∈R then a ≠ b D.

Find x and y given (2x, x + y) = (6, 2). A. x=2,y=1 B.

x=3,y=-1

C. x=2,y=-1 D. x=3,y=1 x=2,y=1

Domain of a relation symbolically written as _______. A. B.

Dom (R) = {a ∈ A | (a, b) ∈ R}

C. Dom(R) = {b ∈ B | (a, b) ∈ R} D. Dom (R) = {a ∉ A | (a, b) ∈ R} Let A = {0,1}and B = {1}.Let R and S be two binary relations on Cartesian product of A and B such that R={(0,1)} and S ={(1,1)}.Then R intersection S = ________________ . A. {1,1} B. {(0,1)} C. {0,1} D.

empty

If x ≡ -10 (mod 15) Which of the following integers are valid solution for x ?

A. B. C. D.

Let R = {(1, 2), (3, 4), (5, 6), (7, 8)}. Range of the inverse of the relation is ________. A.

{1, 3, 5, 7}

B. {5, 6, 7, 8} C. {1, 2, 3, 4} D. {2, 4, 6, 8}

Let R be a relation on a set A. If R is symmetric then its compliment is

A. B. Symmetric C. Reflexive D.

If A={1 , 2 , 3} is a set and R = {(1 , 2) , (2 , 2) , (2 , 1)} is a relation on A, R is A. Reflexive B.

Symmetric

C. D.