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)

We are provided with ;

And we need no find . At first Let me tell you that here represents the union of the set B and C.And represents the cardinal no. of the respective set or no. of elements present in the respective set.So let's find the set first

As we know that ;

Where 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 :-

So , . Now , putting the values in the formula;

The answer is in the image 

The answer is in the image 

The answer is in the image 

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The answer is in the image 

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students  

Area of rectangle= L*b

here,

L=12.4 cm

b= 8.8 cm

A= L*b

= 12.4 * 8.8 = 109.12 cm^2

Given height of gymnasium is 5/6 height of 30 foot ball

therefore height of gymnasium=5/6 * 30

=25 feet