In a group of 400 people, 250 can speak Hindi and 200 can speak English.How many can speak both Hindi and English?

Let n(U) = 700, n(A) = 200, n(B) = 300 and \(n(A\cap B)\) = 100 .Find \(n({ A }^{ ' }\cap { B }^{ ' })\).

Let F₁ be the set of parallelograms, F₂ be the set of rectangles, F₃ be the set of rhombus and F₄ be the set of squares. Then, show that F₁ is equal to the union of all sets.

If U={a,b,c,d,e,f}, A={a,b,c}, B={c,d,e,f}, C={c,d,e}, D={d,e,f}, then tabulate the following set U\(\cap \)D

If U={a,b,c,d,e,f}, A={a,b,c}, B={c,d,e,f}, C={c,d,e}, D={d,e,f}, then tabulate the following set (U\(\cap \phi \))'

In a school  there are 20 teachers who teach Maths or Physics.Out of these, 12 teach Maths and 4 teach Physics and Maths.How many teach Physics?

Let A, B and C be three sets, If A\(\in\)B and B \(\subset\) C, is it true that A \(\subset\) C? If not, give an example.

If set A = {1,3,5}, then find the number of elements in P{P(A)}.

Write the following as intervals.
{x : x \(\in\) R, -12< x < -10}

Write the following as intervals.
{x : x \(\in\) R, 0 \(\le\) x < 7}

There are 60 students in a Mathematics class and 90 students in Physics class.Find the number of students which are either in Physics class or Mathematics class in the following case.Two classes meet at the same hour.

There are 60 students in a Mathematics class and 90 students in Physics class.Find the number of students which are either in Physics class or Mathematics class in the following case.Two classes meet at different hours and 30 students are enrolled in the courses.

In a group of 50 students, the number of students studying French, English and Sanskrit were found to be as follows French = 17, English = 13, Sanskrit = 15, French and  English = 9 and Sanskrit = 4, French and Sanskrit = 5  and English, French and Sanskrit = 3.
Then, find the number of students who study French only.

Prove that  \(A-(B\cap C)=(A-B)\cup (A-C).\)

Find the intersection of each of the following pairs of sets.
A = {e, f, g}, B = \(\phi\)

Prove that n (n+1) (n+5) is a multiple of 3, for all \(n\in N\)

For every positive integer n, prove that 7ⁿ-2ⁿ is divisible by 5.

There are 200 individuals with a skin disorder, 120 has been exposed to chemical C_1, 50 to chemical C₂ and 30 to both the chemicals C _1 ,  C ₂  . FInd  the number of individuals exposed to chemical C₂ but  not chemical C_1.

If A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B= {2, 4,......18} and N, the set of natural numbers is the universal set, then prove that A'\(\cup\){(A\(\cup\)B)\(\cap\)B'} = N.

Taking the set of a natural numbers as the universal set, write down the complements of the set.
{x : x \(\in \) N, 2x + 1>10}

\(If\ f(x)=\frac { 1 }{ 2x+1 } x\neq -\frac { 1 }{ 2 } ,\text{then show that}\) \(\\ f(f(x))=\frac { 2x+1 }{ 2x+3 } ,\text{provide that}x\neq -\frac { 3 }{ 2 } .\)

Let A and B be two sets. Using properties of set prove that A\(\cap \)B=\(\phi \)\(\Rightarrow \)A\(\subseteq \)B

Write the following as intervals and also represent on the number line
x:x∈R,−5