Functions Part 1

x={f:A→B,f is one - one }
y={g:A→A×B,g is one one }
Number of elements in A=3 i.e. |A|=3
Similarly, |B|=5
Then, |A×B|=|A|×|B|=3×5=15
Now, number of one-one function from A to B will be
‌5P3=‌

5!

(5−3)!

=‌

5!

2!

=5×4×3=60
∴‌‌x=60
Now, number of one-one function from A to A×B will be
‌‌=‌15P3=‌

15!

(15−3)!

=‌

15!

12!

‌‌=15×14×13=2730
y=2730
Thus, 2×(2730)=91×(60)
2y=91x