mathematics-class-11-unit-01-chapter-02-set-theory-l-2-3-kumxqqpggtw

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Set theory  lecture-2 </B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Distributive law</B></Primary></p>
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<p>$A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)$</p>
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<p>$A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)$</p>
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<p><span style="color:red">$A\cap B$</span></p>
<p><span style="color:blue">$A \cap C$</span></p>
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Recall: representation of sets$\to$ Intervals in$\mathbb{R}$$\to$ Proper subset$\to$ Super set$\to$ Properties of union $\to$ Properties of intersection$\to$<span style="color:blue"> Distributive law</span>$\to$ Properties of complement$\to$ De Morgan's laws$\to$ Number of elements in the union$\to$ Proof of number of elements in the union$\to$Example$\to$ Proof of   n $(A\cup B\cup C)$ $\to$ Solution$\to$ Problem $\to$ Notations
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Set theory  lecture-2 </B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>De morgan’s laws</B></Primary></p>
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<p>i. $(AUB)’ = A’∩ B'$</p>
<p>ii. $(A∩B)’ = A’U B'$</p>
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Recall: representation of sets$\to$ Intervals in$\mathbb{R}$$\to$ Proper subset$\to$ Super set$\to$ Properties of union $\to$ Properties of intersection$\to$ Distributive law$\to$ Properties of complement$\to$<span style="color:blue"> De Morgan's laws</span>$\to$ Number of elements in the union$\to$ Proof of number of elements in the union$\to$Example$\to$ Proof of   n $(A\cup B\cup C)$ $\to$ Solution$\to$ Problem $\to$ Notations
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Set theory  lecture-2 </B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Number of elements in the union</B></Primary></p>
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<p>Let $A$ and $B$ are two finite sets such that $A∩B=\phi$.<br>
Then $n(AUB)=n(A)+n(B)$</p>
<p>$n(A)\rightarrow$ number of elements in $A$</p>
<p>$n(B)\rightarrow$ number of elements in $B$</p>
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<footer style='font-size:18px'>
Recall: representation of sets$\to$ Intervals in$\mathbb{R}$$\to$ Proper subset$\to$ Super set$\to$ Properties of union $\to$ Properties of intersection$\to$ Distributive law$\to$ Properties of complement$\to$ De Morgan's laws$\to$ <span style="color:blue">Number of elements in the union</span>$\to$ Proof of number of elements in the union$\to$Example$\to$ Proof of   n $(A\cup B\cup C)$ $\to$ Solution$\to$ Problem $\to$ Notations
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Set theory  lecture-2 </B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>$\text{Proof of} \ n(A \cup B \cup C)$</B></Primary></p>
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<p>By (ii) in (i),</p>
<p>$n(A∩B∩C)=n(A)+n(B)+n(C)-n(A∩B)-n(B∩C)-n(A∩C)+n(A∩B∩C)$</p>
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<hr>
<footer style='font-size:18px'>
Recall: representation of sets$\to$ Intervals in$\mathbb{R}$$\to$ Proper subset$\to$ Super set$\to$ Properties of union $\to$ Properties of intersection$\to$ Distributive law$\to$ Properties of complement$\to$ De Morgan's laws$\to$ Number of elements in the union$\to$ Proof of number of elements in the union$\to$Example$\to$ <span style="color:blue">Proof of   n $(A\cup B\cup C)$</span> $\to$ Solution$\to$ Problem $\to$ Notations
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Set theory  lecture-2 </B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Example</B></Primary></p>
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<p>$400$ People who speaks either English or Hindi or Both.</p>
<p>$250$ people : speak Hindi</p>
<p>$200$ people : speak English</p>
<p>How many speak both languages?</p>
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<footer style='font-size:18px'>
Recall: representation of sets$\to$ Intervals in$\mathbb{R}$$\to$ Proper subset$\to$ Super set$\to$ Properties of union $\to$ Properties of intersection$\to$ Distributive law$\to$ Properties of complement$\to$ De Morgan's laws$\to$ Number of elements in the union$\to$ Proof of number of elements in the union$\to$<span style="color:blue">Example</span>$\to$ Proof of   n $(A\cup B\cup C)$ $\to$ Solution$\to$ Problem $\to$ Notations
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