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$Q. 13 If A={1,2,3,4},B={3,4,5,6}, U={1,2,3,4,5,6} then prove De Mlorgan: law. De Morgan's law: first Jaw: (A uu B)^(')=A^(')nnB^(') Second Jdw: (A nn B)^(')=A^(')uuB^(')$

Q. $13$ If $A=\{1,2,3,4\}, B=\{3,4,5,6\}$ , $U=\{1,2,3,4,5,6\}$ then prove De Mlorgan: law. $\newline$ De Morgan's law: $\newline$ first Jaw: $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$ $\newline$ Second Jdw: $(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$

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Transformations of quadratic functions

Full solution

Q. Q.

13

If

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

,

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

then prove De Mlorgan: law.

\newline

De Morgan's law:

\newline

first Jaw:

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

\newline

Second Jdw:

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

Find Complement of A and B: First, let's find the complement of A and B in U. $\newline$ $A' = \{\text{elements in U not in A}\} = \{5, 6\}$ $\newline$ $B' = \{\text{elements in U not in B}\} = \{1, 2\}$
Find Union of A and B: Now, 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: Next, we find the complement of $A \cup B$ in $U$ .
$(A \cup B)' = \{\text{elements in } U \text{ not in } A \cup B\} = \{\}$
But this is wrong, there should be elements here. I made a mistake.

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