If 𝐴 = {2, 3}, 𝐵 = {4}, 𝐶 = {5}, verify that 𝐴 x (𝐵 ⋃ 𝐶)

To verify 𝐴 x (𝐵 ⋃ 𝐶), we first need to understand what these symbols mean.

1. 𝐴, 𝐵, 𝐶 are sets. 𝐴 contains elements 2 and 3, 𝐵 contains element 4, and 𝐶 contains element 5.
2. "⋃" is the union of two sets, which means it combines all the elements from both sets, but removes any duplicates.
3. "x" represents the Cartesian product of two sets, which is a set of all ordered pairs (a, b) where a is in the first set and b is in the second set.

Step 1: Find 𝐵 ⋃ 𝐶 Since 𝐵 = {4} and 𝐶 = {5}, their union will be {4, 5} because there are no duplicates.

Step 2: Find 𝐴 x (𝐵 ⋃ 𝐶) Now we need to find the Cartesian product of 𝐴 and the union of 𝐵 and 𝐶. 𝐴 = {2, 3} and 𝐵 ⋃ 𝐶 = {4, 5} So, 𝐴 x (𝐵 ⋃ 𝐶) will be {(2, 4), (2, 5), (3, 4), (3, 5)}.

So, we have verified that 𝐴 x (𝐵 ⋃ 𝐶) = {(2, 4), (2, 5), (3, 4), (3, 5)}.