Question

Let \[A = \left\{ x: x \in N \right\}, B = \left\{ x: x - 2n, n \in N \right\}, C = \left\{ x: x = 2n - 1, n \in N \right\}\] and D = {x : x is a prime natural number}. Find: \[B \cap C\]

Answer 1

\[A = \left\{ x: x \in N \right\} = {1, 2, 3, . . . }\]
\[B = \left\{ x: x - 2n, n \in N \right\} = {2, 4, 6, 8, . . . } \]
\[C = \left\{ x: x = 2n - 1, n \in N \right\} = {1, 3, 5, 7, . . . }\]
D = {x:x is a prime natural number.} = {2, 3, 5, 7,...} 

\[B \cap C\]=\[\phi\]