Class 11

Math

Calculus

Sets

If A and B are disjoint then $(A∩B)_{′}=$_______

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Let $A={1,2,{3,4},5}$. Which of the following statements are incorrect and why?(i) ${3,4}⊂A$

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

Let X = {Rani, Geeta, Akbar} be the set of students of Class XI who are in school hockey team. Let Y = {Geeta, David, Ashok} be the set of students from Class XI who are in the school football team. Find X$∪$Y and interpret the set

If X and Y are two sets such that X has 40 elements, $X∪Y$has 60 elements and $X∩Y$has 10 elements, how many elements does Y have?

Let$U={1,2,3,4,5,6,7,8,9},A={2,4,6,8}andB={2,3,5,7}˙$ Verify that: $(A∪B)_{_{′}}=A_{′}∩B_{′}$ (ii) $(A∩B)_{_{′}}=A_{prime}∪B_{p}rime$

Show that $A∩B=A∩C$need not imply $B=C$.

For any sets A and B. show that $P(A∩B)=P(A)∩P(B)˙$

Show that if $A⊂B$, then $C−B⊂C−A$ .