Write the following intervals in set-builder form:

 (i) (–3, 0) 

(ii) [6, 12] 

(iii) (6, 12] 

(iv) [–23, 5)  

What universal set (s) would you propose for each of the following? 

(i) The set of right triangles 

(ii) The set of isosceles triangles 

If A and B are two sets such that A ⊂ B, then what is A ∪ B? 

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of

 the following may be considered as universals set (s) for all the three sets A, B and C 

(i) {0, 1, 2, 3, 4, 5, 6} 

(ii) Φ 

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} 

(iv) {1, 2, 3, 4, 5, 6, 7, 8} 

Let A = {a, b}, B = {a, b, c}. Is A ⊂ B? What is A ∪ B? 

Find the union of each of the following pairs of sets: 

(i) X = {1, 3, 5}; Y = {1, 2, 3} 

(ii) A = {a, e, i, o, u}; B = {a, b, c} 

(iii) A = {x: x is a natural number and multiple of 3} B = {x: x is a natural number less than 6} 

(iv) A = {x: x is a natural number and 1 < x ≤ 6} B = {x: x is a natural number and 6 < x < 10} 

(v) A = {1, 2, 3}; B = Φ 

Let A and B be sets. 

If A ∩ X = B ∩ X = Φ 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) 

Show that 

A ∩ B = A ∩ C 

need not imply B = C. 

Using properties of sets show that 

(i) A ∪ (A ∩ B) = A 

(ii) A ∩ (A ∪ B) = A. 

Show that for any sets A and B, 

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