Verify (A ∩B)′ = A′ ∪ B′ using Venn diagrams. $[5]$

Open in App

Solution

Lets take the LHS first,
(A ∩B)'
Step 01: Draw (A ∩B)
(1) $ (A \cap B) $ $[1]$
Step 02:Draw (A ∩B)'
(2) $[1]$
Now, let's move to RHS
Step 03: Draw A'

$[1]$
Step 04: Draw B'(4) $[1]$
Step 05: Draw A′ ∪ B′
$[1]$
Since (2) = (5)
(A ∩B)′ = A′ ∪ B′ is verified.

Suggest Corrections

Similar questions

(A \cap B)^{'} = A^{'} \cup B^{'}

(A \cup B)^{'} = A^{'} \cup B^{'}

Use Venn diagrams to verify De Morgan’s law of complementation (A $\cup$ B)’ = A’ $\cap$ B’

A ∖ (B \cap C) = (A ∖ B) \cup (A ∖ C)

A ∖ (B \cap C) = (A ∖ B) \cup (A ∖ C)

Join BYJU'S Learning Program