If A = {x : x ∈ W, x < 2}, B = {x : x ∈ N, 1 < x < 5} and C = {3,5}, then A × (B ∩ C)
Question
If
\[ A = \{x : x \in W,\ x<2\}, \]
\[
B = \{x : x \in N,\ 1
and
\[
C = \{3,5\},
\]
then
\[
A \times (B \cap C)= \ ?
\]
First find each set.
Since \( W \) denotes whole numbers,
\[
A=\{0,1\}
\]
Now,
\[
B=\{2,3,4\}
\]
and
\[
C=\{3,5\}
\]
Find the intersection:
\[
B\cap C=\{3\}
\]
Now compute the Cartesian product:
\[
A\times(B\cap C)=\{0,1\}\times\{3\}
\]
Therefore,
\[
A\times(B\cap C)=\{(0,3),(1,3)\}
\]
Hence, the required answer is:
\[
\boxed{\{(0,3),(1,3)\}}
\]
Solution