What is the mathematical symbol proof of
If A is a subset of B then P(B|A)=1 and P(A|B)=P(A)/P(B)
If A is a subset of B, then AnB = A.
Thus,
P(B|A) = P(AnB)/P(A) = P(A)/P(A) = 1
P(A|B) = P(AnB)/P(B) = P(A)/P(B)
What is the mathematical symbol proof of If A is a subset of B then P(B|A)=1...
For odd registration numbers, demonstrate through mathematical proof that the expected value for the binomial (n, p) random variable X is E [X] = np and variance Var[X] = np(1 − p).
write a formal proof and state witch proof style you
use
1 1 + +...+ 3.4 n-2 6. (5 pts.) a. What is the first n that P(n) is true? P(n): 4.5 n(n+1) 3n+3 b. (20 pts. Use mathematics induction to prove (write a formal proof). For all ne N, where n is greater than or equal to? (the answer form part a) P(n) is true, where 1 1-2 P(n): Be sure to state which of the three types of...
9) What does the mathematical symbol Il represent? 10 Let X = (1, 3, 5) and Y = {a,b,c,d). Define g: X by the following arrow diagram. Y . a. Write the domain of g and the co-domain of g. b. Find g(1), :.! c. What is the range of g? d. Is 3 an inverse image of a?" e. What is the inverse image of b? 1. Represent g as a set of ordered pairs.
Let A be a nonempty finite subset of R. Use mathematical induction on the number of members of A to show that A has both a largest and a smallest member.
Mathematical Analysis help
2. If J is uniformly continuous on a bounded subset A of R, prove that f is bounded on A.
True or False:P(A|B)=1-P(A|B') . Verify your choice with a proof (if true) or counterexample (if false) True or False:P(A|B)=1-P(A'|B) . Verify your choice with a proof (if true) or counterexample (if false)
10. In the proof that the 3SAT problem is polynomially reducible to the SUBSET SUM problem, put of the 3SAT problem) to a set of numbers and a target number as input of the SUBSET_SUM problem arbitrary boolean expression in 3CNF (in- we convert an (a) Please ilustrate the conversion by giving the set of numbers and the target number that will be obtained from the following boolean expression: (T ) . (b) The original boolean expression is satisfiable. reduction...
Mathematical Logic
Proof in paragraph form
5) Prove that if n is odd, then n2 leaves a remainder of 1 when it is divided by 4
I need help with this question.
(Computer Algorithms)
10. (10 %) Use proof by mathematical induction to show that N +1
7. Give a proof by contradiction that for any subset S of 26 cards from a 52 card deck ( a 52 card deck is composed of 4 suits of 13 cards each), there is a suit such that S has at least 7 cards of that suit. This is an application of the pigeonhole principle.