NCERT Class XI Mathematics - Sets - Solutions
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Question : 67
Total: 73
Show that A ∩ B = A ∩ C need not imply B = C.
Solution:
Let A = {1, 2, 3, 4}, B = {2, 3, 4, 5, 6}, C = {2, 3, 4, 9, 10}
∴ A ∩ B = {1, 2, 3, 4} ∩ {2, 3, 4, 5, 6} = {2, 3, 4}
A ∩ C = {1, 2, 3, 4} ∩ {2, 3, 4, 9, 10} = {2, 3, 4}
Now we have A ∩ B = A ∩ C. But B ≠ C.
∴ A ∩ B = {1, 2, 3, 4} ∩ {2, 3, 4, 5, 6} = {2, 3, 4}
A ∩ C = {1, 2, 3, 4} ∩ {2, 3, 4, 9, 10} = {2, 3, 4}
Now we have A ∩ B = A ∩ C. But B ≠ C.
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