Empty Relations

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. 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.

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. 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. $R=\left\{\right(a,b):a+b=11:a,b\in A\}$