State true or false-P A - P B - P A - B

Let A =0,1 amp; B=1,2 ∴ A ∪ B ={ 1,2,3 } P(A) = ϕ, 0, 1, 0,1 P(B) =ϕ, 1,2,1,2 P(A ∪ B) =ϕ, 0,,1,2,0,1,1,2,0,2,0,1,2 P(A)∪ P(B) =0, 0,1,0,1,2,1,2 Clearly P(A) ...

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Byju's Answer

Standard XII

Mathematics

Complement

State true or...

Question

State true or false:
$P (A) \cup P (B) = P (A \cup B)$

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Solution

Let A ={0,1} & B={1,2}
$∴ A \cup B = {1, 2, 3}$
P(A) ={ $ϕ$ , {0}, {1}, {0,1}}
P(B) ={ $ϕ$ , {1},{2},{1,2}}
$P (A \cup B)$ ={ $ϕ$ , {0,},{1},{2},{0,1},{1,2},{0,2},{0,1,2}}
$P (A) \cup P (B)$ ={0, {0},{1},{0,1},{2},{1,2}}
Clearly $P (A) \cup P (B) \neq P (A \cup B)$

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Similar questions

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In the figure given below, PA and PB are tangents to the circle from point P, Where PA = PB.

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The probabilities of three mutually exclusive events A, B, C are

P (A) = \frac{2}{3}, P (B) = \frac{1}{4}, P (C) = \frac{1}{6} .

Q. If A and B are two events such that

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Q. Assume that

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Is it true that for any sets

A

and

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P (A \cup B) = P (A \cap B)

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.If this is true enter 1,else enter 0

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State true or false: P(A)∪P(B)=P(A∪B)

Let A ={0,1} & B={1,2} ∴A∪B={1,2,3} P(A) ={ ϕ, {0}, {1}, {0,1}} P(B) ={ϕ, {1},{2},{1,2}} P(A∪B) ={ϕ, {0,},{1},{2},{0,1},{1,2},{0,2},{0,1,2}} P(A)∪P(B) ={0, {0},{1},{0,1},{2},{1,2}} Clearly P(A)∪P(B)≠P(A∪B)

State true or false:
$P (A) \cup P (B) = P (A \cup B)$

Let A ={0,1} & B={1,2}
$∴ A \cup B = {1, 2, 3}$
P(A) ={ $ϕ$ , {0}, {1}, {0,1}}
P(B) ={ $ϕ$ , {1},{2},{1,2}}
$P (A \cup B)$ ={ $ϕ$ , {0,},{1},{2},{0,1},{1,2},{0,2},{0,1,2}}
$P (A) \cup P (B)$ ={0, {0},{1},{0,1},{2},{1,2}}
Clearly $P (A) \cup P (B) \neq P (A \cup B)$