Question

यदि $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9 \}$, $A = \{2, 4, 6, 8\}$ और $B = \{ 2, 3, 5, 7\}$, तो सत्यापित कीजिए कि: (i) $(A \cup B)^{'} = A^{'} \cap B^{'}$ (ii) $(A \cap B)^{'} = A{'} \cup B{'}$

Answer 1

Hello mate

this is very difficult question

It will take time to answer

Answer 2

Answer:

Step-by-step explanation:

(i). A∪B = {2, 4, 6, 8} ∪ {2, 3, 4, 5, 6,7, 8}

बांया तरफ का हल:

(A∪B)' = U - (A∪B) = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 4, 5, 6, 7, 8} = {1, 9}

A' = U - A = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 4, 6, 8} = {1, 3, 5, 7, 9}

B' = U - B = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 5, 7} = {1, 4, 6, 8, 9}

दांया तरफ का हल :

A'∩B' = {1, 3, 5, 7, 9} ∩ {1, 4, 6, 8, 9} = {1, 9}

अतः  (A∪B)' = A'∩B'

(II). बांया तरफ का हल:

(A∩B)'

(A∩B)' = {2, 4, 6, 8} ∩ {2, 3, 5, 7} = {2}

(A∩B)' = {1, 2, 3, 4, 5, 6,7, 8, 9} - {2} = {1, 3, 4, 5, 6, 7, 8, 9}

दांया तरफ का हल :

A'∪B' = {1, 3, 5, 7, 9} ∪ {1, 4, 6, 8, 9} = {1, 3, 4, 5, 6, 7, 8, 9}

अतः (A∩B)' = A'∪B'