If A={1,2,3,4}, B={3,4,5,6}, U={1,2,3,4,5,6} then prove De Mlorgan's law. De Morgan's law: first Law: (A uu B)^(')=A^(')nnB^(') Second Law: (A nn B)^(')=A^(')uuB^(')

Find Union of A and B: First, let's find the union of A and B. A ∪ B = {1, 2, 3, 4} ∪ {3, 4, 5, 6} = {1, 2, 3, 4, 5, 6}Find Complement of Union in U: Now, let's find the complement of A ∪ B in U. (A ∪ B)' = U - (A ∪ B) = {1, 2, 3, 4, 5, 6} - {1, 2, 3, 4, 5, 6} = {}Find Complements of A and B: Next, find the complements of A and B in U separately. A' = U - A = {1, 2, 3, 4, 5, 6} - {1, 2, 3, 4} = {5, 6} B' = U - B = {1, 2, 3, 4, 5, 6} - {3, 4, 5, 6} = {1, 2}Find Intersection of Complements: Now, let's find the intersection of A' and B'. A' ∩ B' = {5, 6} ∩ {1, 2} = {}

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If $A=\{1,2,3,4\},B=\{3,4,5,6\}, U=\{1,2,3,4,5,6\}$ then prove De Morgan's law. $\newline$ De Morgan's law: first Law: $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$ Second Law: $(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$

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Q. If

A=\{1,2,3,4\},B=\{3,4,5,6\}, U=\{1,2,3,4,5,6\}

then prove De Morgan's law.

\newline

De Morgan's law: first Law:

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

Second Law:

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

Find Union of A and B: First, let's find the union of A and B. $A \cup B = \{1, 2, 3, 4\} \cup \{3, 4, 5, 6\} = \{1, 2, 3, 4, 5, 6\}$
Find Complement of Union in U: Now, let's find the complement of $A \cup B$ in $U$ . $(A \cup B)' = U - (A \cup B) = \{1, 2, 3, 4, 5, 6\} - \{1, 2, 3, 4, 5, 6\} = \{\}$
Find Complements of A and B: Next, find the complements of A and B in U separately. $\newline$ $A' = U - A = \{1, 2, 3, 4, 5, 6\} - \{1, 2, 3, 4\} = \{5, 6\}$ $\newline$ $B' = U - B = \{1, 2, 3, 4, 5, 6\} - \{3, 4, 5, 6\} = \{1, 2\}$
Find Intersection of Complements: Now, let's find the intersection of $A'$ and $B'$ . $A' \cap B' = \{5, 6\} \cap \{1, 2\} = \{\}$