3. If A = {2, 4, 6, 8, 10} and B = {3, 6, 9, 12, 15}, find A – B and B – A.
4. If A and B are two sets such that A Ì B then what is A È B?
5. Let A = {x : x is a natural number}, B = {x : x is an even natural number}
C = {x : x is an odd natural number} and D = {x : x is a prime number}
Find A Ç B, A Ç C, A Ç D, B Ç C, B Ç D and C Ç D.
6. If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and D = {5, 10, 15, 20}, find
(i) A – B (ii) A – C (iii) A – D (iv) B – A (v) C – A
(vi) D – A (vii) B – C (viii) B – D (ix) C – B (x) D – B
7. State whether each of the following statements is true or false. Justify your answers.
(i) }2, 3, 4, 5} and {3, 6} are disjoint sets.
(ii) {a, e, i, o, u} and {a, b, c, d} are disjoint sets.
(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.
2.7 EQUAL SETS
Consider the foll
Consider the following sets.
A = {Sachin, Dravid, Kohli}
B = {Dravid, Sachin, Dhoni}
C = {Kohli, Dravid, Sachin}
What do you observe in the above three sets A, B and C? All the players that are in A
are in C. Also, all the players that are in C are in A. Thus, A and C have same elements but some
elements of A and B are different. So, the sets A and C are equal sets but sets A and B are not
equal.
Two sets A and C are said to be equal if every element in A belongs to C (i.e.AÍ C)
and every element in C belongs to A (i.e.C Í A).
If A and C are equal sets, then we write A = C. Thus, we can also write that C Í A and
A Í C ÛA = C. [Here Û is the symbol for two way implication and is usually read as, if and
only if (briefly written as “iff”]