If relations R1 and R2 from set A to set B are defined as R1= (1 , 2) , (3 , 4) , (5 , 6) and R2= (2 , 1) , (4 , 3) , (6 , 5) , then n(A × B) can be equal to

Question

If relations R1 and R2 from set A to set B are defined as R1= (1 , 2) , (3 , 4) , (5 , 6) and R2= (2 , 1) , (4 , 3) , (6 , 5) , then n(A × B) can be equal to (A) 35 (B) 53 (C) 91 (D) 55

Tardigrade Admin · Accepted Answer

n(A × B)=n(A)× n(B) Now minimum n(A)=6 and minimum n(B)=6 ⇒ n(A)× n(B) can be equal to 7× 13=91

Q. If relations $R_{1} an d R_{2}$ from set $A$ to set $B$ are defined as $R_{1} = {(1, 2), (3, 4), (5, 6)}$ and $R_{2} = {(2, 1), (4, 3), (6, 5)}$ , then $n (A \times B)$ can be equal to

$35$

$53$

$91$

$55$

$n (A \times B) = n (A) \times n (B)$
Now minimum $n (A) = 6$ and minimum $n (B) = 6$
$\Rightarrow n (A) \times n (B)$ can be equal to $7 \times 13 = 91$

Q. If relations R1​andR2​ from set A to set B are defined as R1​={(1,2),(3,4),(5,6)} and R2​={(2,1),(4,3),(6,5)} , then n(A×B) can be equal to

35

53

91

55