Eduprobe
Question:
Show that A∩B = A∩C need not imply B = C
Solution:
Let A = {0, 1}, B = {0, 2, 3}, C = {0, 4, 5}
So, A∩B = {0} and A∩C = {0}
Here, A∩B = A∩C = {0}
However, B ≠ C as 2 ∈ B and 2 ∉ C
Let A = {0, 1}, B = {0, 2, 3}, C = {0, 4, 5}
So, A∩B = {0} and A∩C = {0}
Here, A∩B = A∩C = {0}
However, B ≠ C as 2 ∈ B and 2 ∉ C