05-28-2014, 05:49 PM
MTH202 Discrete Mathematics VU Online Quiz No. 02 Solution and Discussion Fall Spring 2014
. Let A = {1, 2, 3, 4} and define a relation R on A by R = {(1, 1), (1, 2), (1, 3), (2, 3)}. Then which one of the following is a correct statement about R:
a) r is transitive
b) r is REflexive
c) r is both Tr, and reflex ANS (but not sure)
d) r is neithr Tr, n Reflex.
2. Let A = {1,2,3,4} and define the relation R on A by R = {(1,2), (2,3), (3,3), (3,4)}.Then ________
Which relations below are not functions?
a. {(3,90),(4,54),(6,71),(8,90)}
b. {(13,14),(13,5),(16,7),(18,13)} ANS
3. R is not symmetric iff there are elements a and b in A such that ____________ .
a) (a, b) belongs to R but (b, a) does not belong to R ANS
b) (a, b) belongs to R but (b, a) belongs to R
4. Let X = {2,4,5} and Y={1,2,4 }and R be a relation from X to Y defined by R = {(2,4), (4,1), (a,2)}. For what value of ‘a ‘ the relation R is a function ?
a) 1 b) 2 c) 3 d) 5 ANS
5. Let f(x)=x and g(x)=-x for all x belongs to R,then f+g(x)is.......
a) -2x, b) -x, c) 0 ANS d)2x
6. Let A = {2, 3, 4} and B = {2,6,8}and let R be the “divides” relation from A to B i.e. for all (a,b) belong to (Cartesian product of A and B),a R b iff a | b (a divides b).Then
a) R = {(2,2), (2,6), (2,8), (3,6), (4,8)} ANS
b) R = {(2,2), (2,6), (2,8), (3,6), (4,8),(6,8)}
. Let A = {1, 2, 3, 4} and define a relation R on A by R = {(1, 1), (1, 2), (1, 3), (2, 3)}. Then which one of the following is a correct statement about R:
a) r is transitive
b) r is REflexive
c) r is both Tr, and reflex ANS (but not sure)
d) r is neithr Tr, n Reflex.
2. Let A = {1,2,3,4} and define the relation R on A by R = {(1,2), (2,3), (3,3), (3,4)}.Then ________
Which relations below are not functions?
a. {(3,90),(4,54),(6,71),(8,90)}
b. {(13,14),(13,5),(16,7),(18,13)} ANS
3. R is not symmetric iff there are elements a and b in A such that ____________ .
a) (a, b) belongs to R but (b, a) does not belong to R ANS
b) (a, b) belongs to R but (b, a) belongs to R
4. Let X = {2,4,5} and Y={1,2,4 }and R be a relation from X to Y defined by R = {(2,4), (4,1), (a,2)}. For what value of ‘a ‘ the relation R is a function ?
a) 1 b) 2 c) 3 d) 5 ANS
5. Let f(x)=x and g(x)=-x for all x belongs to R,then f+g(x)is.......
a) -2x, b) -x, c) 0 ANS d)2x
6. Let A = {2, 3, 4} and B = {2,6,8}and let R be the “divides” relation from A to B i.e. for all (a,b) belong to (Cartesian product of A and B),a R b iff a | b (a divides b).Then
a) R = {(2,2), (2,6), (2,8), (3,6), (4,8)} ANS
b) R = {(2,2), (2,6), (2,8), (3,6), (4,8),(6,8)}