Home
Class 12
MATHS
Is it true that for any sets A and B, P...

Is it true that for any sets A and B, `P (A) uuP (B) = P (Auu B)`? Justify your answer.

Text Solution

Verified by Experts

Let A= {0,1} and B ={1,2}
`therefore A cup B ={ 0,1,2}`
`therefore A cup B = { 0, 1, 2 } `
P(A) = {0), {0}, {1}, {0, 1}}
P(B)= {`phi`, {1}, {2}, {1,2}}
`P( A cup B) ={ phi {0},{1},{2},{0,1},{1,2},{0,2},{0,1,2}}`
`P(A) cup P(B)={phi, {0}, {1}, {0,1}, {2}, {1,2}} `
`therefore P(A) cup P(B) ne P ( A cup B)`
Promotional Banner

Topper's Solved these Questions

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 1.2|8 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 1.3|13 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE PUBLICATION|Exercise Solved Exp|11 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Is it true that for any sets A and B, P ( A ) ∪ P ( B ) = P ( A ∪ B ) ? Justify your answer.

If any two sets A and B, (A cup B)' cup(A'cup B) =

For any two sets A and B, A-(A-B) equals

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

For any two sets A and B, prove that P(A) cup P(B) sube P(A cup B)

Is it right to say that sin (A+B) =sin A +sin B ? Justify your answer.

Let A,B and C be three sets. If A in B and B subC, is it true that A subC? Justify your answer by an example.

For any two events A and B, show that, P(A uu B) = P(A) + P(B) - P(A nn B) .

Prove that P(A uu B) = P(A) + P(B) - P(A nn B)

For any two events A and B prove that, P(A cup B) le P(A) + P(B)