Question

Let U = {English, French, History, Math, Physics, Chemistry, Psychology, Drama}, A = {Math, History, Chemistry, English}, B = {Psychology, Drama, French, Chemistry, English}, and C = {Physics, History, French}. Find the following. n(B u C)

Answer 1

We are provided with ;

• ${\sf{U=\{English,\: French,\: History,\: Math,\: Physics,\: Chemistry,\: Psychology,\: Drama\}}}$
• ${\sf{A=\{Math,\: History,\: Chemistry,\: English\}}}$
• ${\sf{B=\{Psychology,\: Drama,\: French,\: Chemistry,\: English\}}}$
• ${\sf{C=\{Physics,\: History,\: French\}}}$

And we need no find ${\bf n(B\cup C)}$ . At first Let me tell you that here ${\sf (B\cup C)}$ represents the union of the set B and C.And ${\sf n(B\cup C)}$ represents the cardinal no. of the respective set or no. of elements present in the respective set.So let's find the set ${\sf (B\cup C)}$ first

${:\implies \quad \sf B\cup C=\{Physics,\: Drama,\: French,\: Chemistry,\: English,\: Psychology,\:History\}}$

${:\implies \quad \bf \therefore \quad \underline{\underline{n(B\cup C)=7}}}$

Alternative Method :-

As we know that ;

• ${\boxed{\bf n(A\cup B)=n(A)+n(B)-n(A\cap B)}}$

Where ${\sf (A\cap B)}$ is the Intersection of A and B or the set of common elements of A and B. So now by same concept , now finding the intersection of B and C :-

${:\implies \quad \sf B\cap C=\{French\}}$

So , ${\sf n(B\cap C)=1}$ . Now , putting the values in the formula;

${:\implies \quad \sf n(B\cup C)=n(B)+n(C)-n(B\cap C)}$

${:\implies \quad \sf n(B\cup C)=5+3-1}$

${:\implies \quad \bf \therefore \quad \underline{\underline{n(B\cup C)=7}}}$