Find A × (B ∩ C) | Cartesian Product of Sets

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

\[ A \times (B \cap C)= \ ? \]

Solution

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:

\[ \boxed{\{(0,3),(1,3)\}} \]

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