Home
Class 12
MATHS
Statement-1 P(A)nnP(B)=P(AnnB), where P(...

Statement-1 `P(A)nnP(B)=P(AnnB)`, where P(A) is power set of set A.
Statement-2 `P(A)uuP(B)=P(AuuB)`.

A

Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1

C

Statement-1 is true, Statement-2 is false

D

Statement-1 is false, Statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
C
Let `x inP(AnnB)`
`iffxsube(AnnB)`
`iffxsubeAandxsubeB`
`iffx inP(A)andx inP(B)`
`iffx inP(A)nnP(B)`
`therefore P(AnnB)subeP(A)nnP(B)`
and `P(A)nnP(B)subeP(AnnB)`
Hence, `P(A)nnP(B)=P(AnnB)`
Now, consider sets A = {1}, B = {2} implies `A uu B` = {1, 2}
`therefore P(A) = {phi, {1}}, P(B)={phi, {2}}`
and `P(AuuB)={phi {1}, {2}, {1,2} ne P(A)uuP(B)}`
Hence, Statement-1 is true and Statement-2 is false.
Promotional Banner

Similar Questions

Explore conceptually related problems

Statement-1 If A and B be the event in a sample space, such that P(A)=0.3 and P(B)=0.2, then P(Acapoverline(B)) cannot be found. Statement-2 P(Auuoverline(B))=P(A)+P(overline(B))-P(Acapoverline(B))

Statement-1 If A is any event and P(B)=1 , then A and B are independent Statement-2 P(AcapB)=P(A)cdotP(B), if A and B are independent

Statement-1 If AuuB=AuuC and AnnB=AnnC , then B = C. Statement-2 Auu(BnnC)=(AuuB)nn(AuuC)

Statement-1 Let A and B be the two events, such that P(AcupB)=P(AcapB) , then P(AcapB')=P(A'capB)=0 Statement-2 Let A and B be the two events, such that P(AcupB)=P(AcapB), then P(A)+P(B)=1

If A, B are two sets, prove that AuuB=(A-B)uu(B-A)uu(AnnB) . and prove that n(AuuB)=n(A)+n(B)-n(AnnB) where, n(A) denotes the number of elements in A.

Statement-1: if A and B are two events, such that 0 lt P(A),P(B) lt 1, then P((A)/(overline(B)))+P((overline(A))/(overline(B)))=(3)/(2) Statement-2: If A and B are two events, such that 0 lt P(A), P(B) lt 1, then P(A//B)=(P(AcapB))/(P(B)) and P(overline(B))=P(A capoverline(B))+P(overline(A) cap overline(B))

If 4P(A) = 6 P(B) = 10 P(A cap B) = 1 then P(B | A) = ……….

Given a non - empty set, X , consider the binary operation ** : P(X) xxP(X) rarr P(X) given by A **B = Acap B , AAA,B in P(X) , where P(X) is the power set X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation ** .

If 6P(A)=8P(B)=14P(AcapB)=1 then the P((A)/(B))= ......

If A and B are two independent events then P(A cap B) = P(A)*P(B) .