Answer to Question #191459 in Discrete Mathematics for ROHAN

Question

(A∪B)

c

(A∪B)c

     

Answer 1

Let,

 

$x ∈ (A ∪ B)^c⇔ x \notin A ∪ B ⇔ x \notin A \text{ and }x \notin B ⇔ x ∈ A^c$

and$x ∈ B^c ⇔ x ∈ A^c ∩ B^c$

Hence, $(A\cup B)^c⇔ (A^c \cap B^c)$