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

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|15 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|2 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

Statement -1 : P(A//B)ge P(A) , then P(B//A) ge P(B) . Statement-2 : P(A//B)=(P(A cap B))/(P(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

Let A and B be two events such that P(A cup B)=P(A cap B) . Then, Statement-1: P(A cap overline(B))=P(overline(A) cap B)=0 Statement-2: P(A)+P(B)=1

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(Acapoverline(B))=P(A)+P(overline(B))-P(Acapoverline(B))

If P(A) = P (B) = x and P(AnnB) = P(A'nnB') = 1/3 , then x = ?

For any two events A and B P(AuuB)=P(A)+P(B)- ……………………...

For a set A, consider the following statements: 1. AuuP(A)=P(A)" 2."{A}nnP(A)=A "3. "P(A)-{A}=P(A) where P denotes power set. Which of the statements given above is/are correct?

Each question has four choices a, b, c, and d, out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. Both the statements are TRUE and statement 2 is the correct explanation of Statement 1. Both the statements are TRUE but Statement 2 is NOT the correct explanation of Statement 1. Statement 1 is TRUE and Statement 2 is FALSE. Statement 1 is FALSE and Statement 2 is TRUE. Statement 1: For events Aa n dB of sample space if P(A/B)geqP(A) , then P(B/A)geqP(B)dot Statement 2: P(A/B)=(P(AnnB))/(P(B)) , (P(B)!=0)dot

If A = null set, then the no. of elements in P(P(P(A))) where P(A) denotes the power set of A is -