Step 1

Solution: \(\displaystyle{n}{\left(\cup\right)}={2400}\)

\(\cup = \left\{1,2,3, .....,2400\right\}\)

\(\displaystyle{2400}\div{3}={800}\)

\(n(s) = n \left\{3 \cdot 1, 3 \cdot 2, .... 3 \cdot 800\right\} = 800\)

\(\displaystyle{n}{\left({t}\right)}={n}{\left({7}\cdot{1},{7}\cdot{2},{7}\cdot{3},\ldots.,{7}\cdot{342}\right)}={342}\)

2394

Step 2

\(\displaystyle{n}{\left({t}\right)}={342}\)

\(\displaystyle{s}\cap{t}\) Multiple of 7 and \(\displaystyle{3}={21}\)

\(\displaystyle{n}{\left({s}\cap{t}\right)}={n}{\left({21}\cdot{1},{21}\cdot{2},\ldots..{21}\cdot{114}\right)}={114}\)

2394

\(\displaystyle{n}{\left({s}\cap{t}\right)}={114}\)