Transitive Relations

Q. 24 Consider the set A={3, 4, 5} and the numbers of null relations, identity relations, universal relations, reflexive relations on A are respectively a, b, c, d then the value of a+b+c+d is?

Q. If three distinct numbers a, b, c are in AP and b-a, c-b, a are in G them a:b:c is equal to

Q. IfA=\{ (4(n-1); n∈ N\} and B= (4-4n:ne Mwhere N is the set of natural numbers, then whichone is true?8.(1) A c B(2) BcA(3) AnB=A

Q. Let A=\{a, b, c, d\}. B and C are two sets such that B ⊂ A, C ⊂ A but B∩ C=Ф. Number ofpossible ordered pairs (B, C) satisfying the above conditions is?

Q.

Let R be a relation on the set N be defined by $\left\{\right(x,y)|x,y|N,2x+y=41\}$. Then R is

1. Reflexive

2. Symmetric

3. Transitive

4. None of these

Q.

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set for all the three sets A, B and C

1. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

2. Φ

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

4. {0, 1, 2, 3, 4, 5, 6, 8}

Q. Q. Find the series 2, 3, 8, 27, 110, 565 (1) 110 (2) 8 (3) 27 (4) 56

Q. 34. let R be the relation on Z defined by R = {(a, b):a, b belongs to Z , a-b is an integer } . find the domain and range of R

Q. Let $R_1$ and $R_2$ be two relations defined as follows:
$R_1=\left\{\right(a,b)\in R^2:a^2+b^2\in Q\}$ and $R_2=\left\{\right(a,b)\in R^2:a^2+b^2\notin Q\}.$ Then

1. Neither $R_1$ nor $R_2$ is a transitive relation
2. $R_1$ and $R_2$ both are transitive relations
3. $R_1$ is transitive but $R_2$ is not a transitive relation
4. $R_2$ is transitive but $R_1$ is not a transitive relation

Q.

Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b²}. Are the following true?

(i) (a, a) ∈ R, for all a ∈ N

(ii) (a, b) ∈ R, implies (b, a) ∈ R

(iii) (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.

Justify your answer in each case.

Q. Consider the set $A=\{1,2,3\}$ and the relation on $A$ as $R=\left\{\right(1,2),(1,3\left)\right\},$ then $R$ is

1. a reflexive relation
2. a symmetric relation
3. a transitive relation
4. None of the above

Q. Let $R=\left\{\right(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6\left)\right\}$ be a relation on the set $A=\{3,6,9,12\}.$ Then the relation is

1. Reflexive and transitive only
2. Reflexive only
3. Reflexive, symmetric and transitive
4. Reflexive but neither symmetric nor transitive

Q. Let R be a relation on the set N of natural numbers defined by $nRm\iff n$ is a factor of m (i.e., n | m). Then R is

1. Reflexive and symmetric
2. Transitive and symmetric
3. Equivalence
4. Reflexive, transitive but not symmetric

Q.

Let $A=\left\{2,3,5,6\right\}$. Then which of the following relations is transitive only?

1. $R=\left\{\left(2,3\right),\left(6,6\right)\right\}$

2. $R=\left\{\left(2,2\right),\left(3,3\right),\left(5,5\right),\left(6,6\right),\left(2,3\right),\left(3,5\right),\left(2,6\right)\right\}$

3. $R=\left\{\left(2,6\right),\left(6,2\right)\right\}$

4. $R=\left\{\left(2,3\right),\left(3,5\right),\left(2,5\right)\right\}$

Q.

Which of the following is an equivalence relation defined on set $A=\left\{1,2,3\right\}$

1. $\left\{(1,1),(1,2),(1,3),(2,2),(2,3),(3,1),(3,2),(3,3)\right\}$

2. $\left\{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2)\right\}$

3. $\left\{(1,1),(2,2),(3,1),(1,3),(3,3)\right\}$

4. $\left\{(1,2),(2,1),(1,3),(3,1)\right\}$