(P1) P(22) = 1 (P2) If A and B are disjoint subsets of 2, then P(A U B) = P(A) + P(B). (P3) If A₁, A2,. are disjoint subsets of N, then 9... 9 PÜAn P(₁.) - n=1 8 | An) = ΣP(An). n=1

Q: Let n EU = Z and p(n): n² + n is an even integer. a. Write the following statement: (Vn) p(n). b. Is…

A: (a) Here, the given statement is: For ∀n∈U=ℤ, p(n):n2+n is an even integer.

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Q: Show that 1+2+3+...+n= ("""). (";"').

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Q: Let M(x) = V3x – 6 and N(x) 2 Find the following: 2 - c) (N o M)(5) d) (No M)(홍) e) (No M)()

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Q: 5s L |(s – 2)

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Q: If P(A) = 0.29 , P(B) = 0.32,  P(A | B) = 0.38 then P(A ∩  B) =

A: Bayes' theorem can be used to compute conditional probabilities and isexpressed as P(A|B)…

Q: snip

A: In a matrix the horizontal arrangements of elements is called rows…

Q: Q:- Show thet B(n, n) B( n+on+=2 1-40

A: The solution is given as

Q: If B C A, then (i) P(AB)=P(A) - P(B), (ii) P(B) ≤ P(A)

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Q: Q4// For all a, b, c in R, Then: O (1) (a-c)s(a-b)+(b-c). (2) la-c|Sla-b|+lb-cl. O (3)…

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Q: If P(A) = P(B) = P(AB), show that P(AB + AB) = 0 [AB = An B]. %3D

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Q: If I (F14)- s²+1 SO is given by? a) V(s? + 1)³

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Q: A drug using to treat a particular disease shows 20% failure rate. If we select a sample of 8…

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Q: If S= {a,b,c} with P(a)= 2P(b)= 4 P(c), find P(a)

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Q: A box has (4) balls. Choose (2) balls one by one with replacement, x is the first chosen and Y is…

A: Given information: No. of balls=4Selection=with replacementNo. of balls to be selected=2

Q: Determine inf H and sup H for H = (-1, 0), H = {0, 1}U(2, 3),

A: As per the guideline i am uploading the first two. For the other two kindly resubmit the questions…

Q: Let gcd(a, b) = d then which of the following is correct (i) (ii) b|d (iii) d|(ax – by) v[p a. All…

A: gcd(a,b) = d  So, by definition, d | a and, d | b  &, d | (ax - by) for all integers x & y…

Q: (p v q) → r = O (p v r)^(¬q v r) O (-p v r)v(q v r) O (-p v r)v(¬q v r) O (-p v r)^(¬q v r)

A: We will find out the required value.

Q: 18

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Q: If P(n-1,3):P(n,4) = 1:9,Findn.

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Q: (d) Show that for all integers n > 1 S(n, 1) = 1 = S(n,n), then, using the above relation (or…

A: Given: n≥1 To find Sn,1=1=Sn,n and show that S4,2=7

Q: Suppose that P(A) = 0.1, P(B) = 0.3, and P(A|B) + P(B|A) = 0.8. Find P(A ∩ B).

A: From the information, given thatThe formula of the conditional probability, for any two events…

Q: (a) If A₁ = {-i, -(i − 1), . . .−3,−2,−1, 0, 1, 2 }, for i = 1, 2, 3,. . . find (i) Un A6 and (ii)…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: X2, ..., Xn, y1, y2, ..., yn, then z is equal to x (A) x + y (B)*+ỹ (C)*+ÿ n (D) x + y 2n

A:

Q: A number is randomly selected from the set {1,2, ·.. , 23!} (note that there is a factorial!). For k…

A: d) Given, Ak = selected number divisible by kP(Ak )=total numbers divided by kTotal numbers=…

Q: P(A) = 0.13, P(B) = 0.47, P (A ∩ B) = 0.05 Find a) P(A|B).   b) P(B|A)

A: P(A) = 0.13, P(B) = 0.47, P (A ∩ B) = 0.05   We know :

Q: 3n-m Let C = n, m EN- Then sup(C) = n?m

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Q: Let B = -3 {CHEMED} 0 Find [x]s 3 3 and x = -8 23

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Q: 6. show that the set A = {P= (₁4₁2) (R³ | 1²4 + √²2+x2 is an open out.

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Q: Suppose X - U(2, 7). Determine P(X > 6 | X > 5). Note: This is a very challenging problem.

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Q: clude four decimal places.) ote: This is a challenging problem. а. Р(X > 5) - || b. Р(X 7| X > 5) =

A: Given Hello. Since your question has multiple, we will solve first question for you. If you want…

Q: 5. A B Suppose that P(A)=0.4, P(B)=0.5 and P(AUB) = 0.42. Are A and B independen Yes, A and B are…

A: Given that  P(A) = 0.4 , P(B) = 0.5