Empty Relations

Q.

What do you mean by reflexive transitive and symmetric relation? Explain with some suitable examples.

Q.

If $R$ is a relation defined as $aRb$, if $\left|a-b\right|>0$, then the relation is

1. Reflexive

2. Symmetric

3. Transitive

4. Symmetric and transitive

Q.

An element of a set can never be a subset of itself. Prove.

Q. Let $A=\{1,2,3,4\}$ and the relation $R$ on set $A$ is defined as $R=\left\{\right(a,b):a+b=10\}.$ Then $R$ is

1. a reflexive relation
2. a symmetric relation
3. a void relation
4. a transitive relation

Q. If $P=\{a,b,c\}$ and $Q=\left\{r\right\}$, form the sets $P\times Q$ and $Q\times P$. Are these two products equal.

Q.

How do you express complex numbers in Cartesian form?

Q. If a relation $R$ is defined on set $A=\{2,3,4,5\}$ as $R=\left\{\right(a,b),a,b\in A:a+b>10\},$ then the relation $R$ is

1. an identity relation
2. a universal relation
3. a void relation
4. not a relation

Q. If a relation $R$ defined on $A=\{1,3,5,7\}$, then which of the following is/are void relation?

1. $R=\left\{\right(a,b):a+b=8:a,b\in A\}$
2. $R=\left\{\right(a,b):2a+b=10:a,b\in A\}$
3. $R=\left\{\right(a,b):2ab=30:a,b\in A\}$
4. $R=\left\{\right(a,b):a+b=11:a,b\in A\}$

Q. If Set $G=\{7,8\}$ and $H=\{5,4,2\}$, then find $G\times H$ and $H\times G$.

Q.

Let R= {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A={1, 2, 3, 4}. The relation R is

1. A function

2. Not symmetric

3. Transitive

4. Reflexive

Q. Let $A=\{1,2,3,4\}$ and the relation $R$ on set $A$ is defined as $R=\left\{\right(a,b):a+b=10\}.$ Then $R$ is

1. a reflexive relation
2. a symmetric relation
3. a void relation
4. a transitive relation

Q. Let $R$ be a relation from $N$ to $N$ defined by $R=\left\{\right(a,b):a,b\in N\text{and}a=b^2\}$. Is the statement true?

(ii) $(a,b)\in R\Rightarrow (b,a)\in R$.

Q. If $B$ is an empty set, then $n\left(B\right)>0.$

1. No
2. Yes

Q.

Empty relation on set A and empty set has the same number of elements

1. True

2. False

Q. Let $A=\{1,2,3,4\}$ and the relation $R$ on set $A$ is defined as $R=\left\{\right(a,b):a+b=10\}.$ Then $R$ is

1. a reflexive relation
2. a symmetric relation
3. a void relation
4. a transitive relation

Q.

State which of the following statement are true or false.

$\left\{1,3,4\right\}$ is same as $\left\{1,7,5,3,4\right\}$

1. True
2. False

Q. Assertion :Let $T$ be the set of all triangle in a plane and $R$ be a relation in $T$ defined by $R=\left\{\right(T_1,T_2):T_1=T_2\}$ is an equivalance relation. Reason: Every equivalence relation is reflexive symmetric and transitive.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q.

Find the number of empty relation we can define on a non empty set A

___

Q.

Empty relation on a set A is the subset of Cartesian product $A\times A$

1. True
2. False

Q.

The relation "Is greater than" on the set {0, -1, 1} is an empty relation.

1. True

2. False

Q.

Which of the following is an empty relation on AxB where A= {0, 2, 5}, B = {1, 4, 7}

1. "Is greater than"

2. "Is less than"

3. "Is a square root of"

4. "Is equal to"

Q.

Empty relation on a set A is the subset of Cartesian product $A\times A$

1. True

2. False

Q.

Find the number of empty relation we can define on a non empty set A

__

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

1. Reflexive but not symmetric
2. Reflexive but not transitive
3. Symmetric and transitive
4. Neither symmetric nor transitive

Q.

Empty relation on a set A is the subset of Cartesian product $A\times A$

1. True
2. False

Q.

Which of the following is an empty relation on AxB where A= {0, 2, 5}, B = {1, 4, 7}

1. "Is greater than"

2. "Is less than"

3. "Is a square root of"

4. "Is equal to"

Q. An empty relation on set A is a subset of the cartesian product $A\times A$.

1. True
2. False

Q.

Which of the following pair of sets are equal sets?

$X=\left\{0,1,2,3\right\}$

$Y=\left\{Wholenumberlessthan4\right\}$

Q. Let $A=\{6,8\},$ $B=\{1,3,5\}$ and $R=\left\{\right(a,b):a\in A,b\in B,a-biseven\}$.
Show that R is an empty relation from A to B.

Q.

The relation "Is greater than" on the set {0, -1, 1} is an empty relation.

1. True

2. False