Class 11

Math

JEE Main Questions

Sets

How many elements has P(A), if $A=φ$?

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State whether each of the following set is finite or infinite:(i) The set of lines which are parallel to the x–axis(ii) The set of letters in the English alphabet(iii) The set of numbers which are multiple of 5(iv) The set of animals living on the earth(v) The set of circles passing through the origin (0, 0)

In a group of $70$ people, $37$ like coffee, $52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

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?

If $U={2,3,5,7,9}$ is the universal set and $A={3,7},B={2,5,7,9},$ then prove that: $(A∪B)_{_{′}}=A_{prime}∩B_{′}$ (ii) $(A∪B)_{_{′}}=A_{prime}∪B_{′}$

Describe the following wets in Roster form: The set of all natural numbers less than 7 ?

Consider the sets $φ,$$A={1,3},$$B={1,5,9},$$C={1,3,5,7,9}$Insert the symbol $⊂$or between each of the following pair of sets : (i) $φB˙˙˙$ (ii) \displaystyle{A}\dot{\dot{\dot{}}}

Assume that $P(A)=P(B)$. Show that $A=B$

Show that the following four conditions are equivalent:(i) $A⊂B$ (ii) $A−B=ϕ$ (iii) $A∪B=B$ (iv) $A∩B=A$