If $A = {2, 3, 5, 7, 11, 13}$ , $B = {5, 7, 9, 11, 15}$ are the subsets of $U = {2, 3, 5, 7, 9, 11, 13, 15}$ , verify De Morgan's laws.

Open in App

Solution

$A = {2, 3, 5, 7, 11, 13}$
$B = {5, 7, 9, 11, 15}$
$U = {2, 3, 5, 7, 9, 11, 13, 15}$
A and B are subset of U.
De Morgan's law
$(1) (A \cup B)^{'} = A^{'} \cap B^{'}$
$(2) (A \cap B)^{'} = A^{'} \cup B^{'}$
$A \cup B = U$
$(A \cup B)^{'} = U^{'}$
$(A \cap B)^{'} = ϕ$
$A^{'} = {9, 15}$
$B^{'} = {2, 3, 13}$
$A^{'} \cap B^{'} = ϕ$
So, $(A \cup B)^{'} = A^{'} \cap B^{'}$
$A \cap B = {5, 7, 11}$
$(A \cap B)^{'} = {2, 3, 9, 13, 15}$
$A^{'} = {9, 15}$
$B^{'} = {2, 3, 13}$
$A^{'} \cup B^{'} = {2, 3, 9, 13, 15}$
So, $(A \cap B)^{'} = A^{'} \cup B^{'}$
Hence De Morgan's law is verified.

Suggest Corrections

Similar questions

U = {- 2, - 1, 0, 1, 2, 3, . . . ., 10}, A = {- 2, 2, 3, 4, 5}

B = {1, 3, 5, 8, 9}

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 = {1, 2, 3}

B = {2, 3, 4, 5}

U = {1, 2, 3, 4, 5, 6, 7, 8}

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

Join BYJU'S Learning Program