Empty Relations

Q.

The void relation on a set $A$ is

1. Reflexive

2. Symmetric and transitive

3. Reflexive and symmetric

4. Reflexive and transitive

Q. Let $A=\{x:x=2n+1,n\in W\}$ and $B=\{y:y=2n,n\in N\}.$ If a relation $R$ is defined from $A$ to $B,$ then which of the following is void relation?

1. $R=\left\{\right(x,y):x+y=11\}$
2. $R=\left\{\right(x,y):x+2y=21\}$
3. $R=\left\{\right(x,y):2x+y=14\}$
4. $R=\left\{\right(x,y):x+y=8\}$

Q.

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

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Q.

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

1. True

2. False

Q.

if empty set is a subset of every set as it is emty then why when contained within brackets the set is non-empty i.e. if it is empty then how can that set be a set?

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 P and Q are two sets such that P has 40 elements, $P\cup Q$ has 60 elements and $P\cap Q$ has 10 elements, how many elements does Q have?

Q.

why an empty set is called a set, when a set is a collection of elements?

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. What is the difference between singleton set and overlapping sets ??