Question

Consider the following in respect of subsets A and B of X 

I. A ⊆ B ⇔ A ∪ B = A

II. (A ∪ B)^c = A^c ∩ B^c

III. A/ B = B/ A  

IV. A ∪ B = A ∩ B, iff  A = B

Which of these are correct? 

(a) I and III (b) I and IV 

(c) II and III (d) II and IV

Answer 1

Correct option is (d)

Explanation:

We know that by the definition of subsets, if A = B 

Then, A ∪ B = A ∩ B, ∀ A, B ∈ X

[ ∵ n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

and by De-Morgan’s law ( A ∪ B)^c = A^c ∩ B^c