Q10 of 86 Page 26

Show that A ∩ B = A ∩ C need not imply B = C.

Let us assume, A = {0, 1}

B = {0, 2, 3}


And, C = {0, 4, 5}


Now, accordingly we have:



And,


∴


Also,


More from this chapter

All 86 →
8

Show that for any sets A and B,

A = (A ∩ B) ∪ (A – B) and A ∪ (B – A) = (A ∪ B)

 9

Using properties of sets, show that:

(i) A ∪ (A ∩ B) = A


(ii) A ∩ (A ∪ B) = A.

 11

Let A and B be sets. If A ∩ X = B ∩ X = f and A ∪ X = B ∪ X for some set X, show that A = B.

(Hints A = A ∩ (A ∪ X) , B = B ∩ (B ∪ X) and use Distributive law)

 12

Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = f.