P (A ∪ B) ≤ P (A) + P (B). This is true we know that Probability is always non-negative(>=0) and P(A ∪ B) = P(A) + P(B) - P(A ∩ B) P(A ∪ B) = P(A) + P(B) - P(A ∩ B) since P(A ∩ B) is >= 0 so, P(A ∪ B) ≤ P(A) + P(B), because P(A ∩ B) is >= 0
Prove/ Disprove : If A and B are any two events, then it is always true...
Prove or disprove: Two events A and B are independent if and only if they are disjoint.
1) True or False: For any two events, A and B, conditional probability is always less than unconditional probability, i.e. P[B|A] < P[B].
3.3 Prove or disprove: The dual graph of the triangulation of a monotone polygon is always a chain, that is, any node in this graph has degree at most two
3.3 Prove or disprove: The dual graph of the triangulation of a monotone polygon is always a chain, that is, any node in this graph has degree at most two
Prove or disprove the following. (a) R is a field. (b) There is
an additive identity for vectors in R^n. (If true, what is
it?)........
1. Prove or disprove the following. (a) R is a field (b) There is an it?) additive identity for vectors in R". (If true, what is (c) There is a is it? multiplicative identity for vectors in R". (If true, what (d) For , , (e) For a, bE R and E R", a(b) =...
3. Prove the statements that are true and give counterexamples to disprove those that are false. (a). Va,b,n E Z* , if a’ =b}(modn) then a =b(modn). (8 points) (b). If p> 2 and q> 2 are prime, then p? +q must be composite. (12 points)
true or false?
If events A and B are independent, then P(AIB) is always equal to zero.
Prove or Disprove that:
If a > 0 and b are two rational numbers, then a' is a rational number.
For any events A, B, C, and D = A∩B∩C prove the following equality: P(D^c) = 1−P(A)·P(B | A)·P(C | A∩B)
Prove or Disprove:
For any natural number n, 7 divides (gn – 2n).
Exercise 2. Prove or disprove the following: a) C € P(A) + CCA b) ACB + P(A) CP(B) c) A=0 + P(A) = 0