Let A={1,2,3,...,10} and B=\left\{\frac{m}{n}:m,n\in A, m<n \text{ and } \gcd(m,n)=1\right\} Then n(B) is equal to:
Explanation
A={1,2,3...10}
B = \left\{\frac{m}{n} : m, n \in A, m < n \text{ and } \gcd(m, n) = 1\right\}
m=1⇒n=2,3,4...109 elements
m=2⇒n=3,5,7,94 elements
m=3⇒n=4,5,7,8,105 elements
m=4⇒n=5,7,93 elements
m=5⇒n=6,7,8,94 elements
m=6⇒n=71 element
m=7⇒n=8,9,103 elements
m=8⇒n=91 element
m=9⇒n=101 element
∴n(B)=31
Explanation
A={1,2,3...10}
B = \left\{\frac{m}{n} : m, n \in A, m < n \text{ and } \gcd(m, n) = 1\right\}
m=1⇒n=2,3,4...109 elements
m=2⇒n=3,5,7,94 elements
m=3⇒n=4,5,7,8,105 elements
m=4⇒n=5,7,93 elements
m=5⇒n=6,7,8,94 elements
m=6⇒n=71 element
m=7⇒n=8,9,103 elements
m=8⇒n=91 element
m=9⇒n=101 element
∴n(B)=31
