Show that If (A ∩ B = ø) then P (A ∪ B) = P (A) + P (B)

Q: Show that if a|b then -a|b.

A:

Q: 4. Prove that it cannot be the case that x E AB and x EB\C. (Hint: prove via contradiction).

A:

Q: In(z,) – In(-V3 – 1) = -In(2) – 1

A: given the argument ∅ of the complex number -3-i as -5π6.and also the modulus of a complex number say…

Q: 6. Prove that if gcd(a , b) = 1, then gcd(a + b, ab) = 1.

A: We need to prove that if gcda,b=1 then gcda+b,ab=1 Let us on the contrary assume that  gcda+b,ab=c…

Q: Q) prove that aset A is non denumerable iland only if AxAXA is nondenumerable

A: In this question, we have to show that a set A is non denumerable if and only if A×A×A is non…

Q: 7. Show that if A and B are similar, then det A = det B. %3D

A:

Q: prove if P>-l then Citp = I+np %3D n€ IN

A: The given statement is not TRUE. Counter example is taking n = 2.

Q: Prove that if gcd(a, b) = 1, then gcd(a + b, ab) = 1.

A:

Q: 6. Prove that if alb and k E Z, then a|(b+ ak).

A:

Q: 3. Find and and y= ivative of

A:

Q: Prove that if |z| = 3, then %3D 5 2z – 1 7 - 13 4+ 22

A: The given is related to complex numbers. The solution is explained below.

Q: Find S ∩ T, (S ∩ T)c, Sc ∩ Tc, S ∪ T, (S ∪ T)c, and Sc ∪ Tc (1) S ={x |x2 > 4}, T = {x |x2 < 9}

A:

Q: Let X: Uc4) out of st andard er dere d uniferm

A: From the given information, X=U4 out of 8 standard ordered uniform and Y=U5out of 8 standard ordered…

Q: Prove that, there is no simple grcup of order 200.

A:

Q: 2. Suppose A is an m x n matrir, x ɛ Rª and Ax = b. Then b is in 1) R" | 2) R™ 3) RmfnT 4) R™n

A: Given :  A is an mxn matrix , x∈Rn and Ax=b   To find :  b is in which space of the given spaces.

Q: Prove that at a party where there are at least two people, there are two people w know the same…

A:

Q: norn rmed M Y is closed if and only if the

A: Given result: Let X, Y be the normed linear spaces  M subspace of X To show: T: M →Y is closed if…

Q: Prove that if A – B – D and B – C – D, then A -C– D.

A:

Q: 1- Suppose A=

A:

Q: Reject Ho if |z| > N

A: We know that  Null hypothesis H0. Alternative hypothesis H1.

Q: Show that if P(A;) = 1 for all i > 1, then P(N1 A¡) = 1.

A: We know that P(Ai) = 1 for i ≥1 Considering P(Ai), i=1,2,3,... to be independent events

Q: 2. Prove that P →¬Q,¬QE¬¬P is not true.

A: To Prove- Prove that P → ¬Q, ¬Q ⊦ ¬¬P is not true.       Concept Used-  A statement is not true or…

Q: 2. Show that p q is congruent to (p - 4)A .

A:

Q: Find all (p, q, r) such that ((p + -4) evaluates to 1.

A:

Q: 4] Let x, YER Using proof by contradiction, prove that VxVy(512y3+8x2y<x³+64y2x⇒8y<x)

A: Introduction:   The procedures to be used when employing direct proof to determine a statement's…

Q: Prove that if n> m - 1, then J,(x) = 2(x/2)"-m

A:

Q: *prove that for . P+2+3+... +n° = 2 n=!,2,3,

A:

Q: Shaa thut the graf of lincs iju fins rom F from E Iwhore is a iomasphic wilh Ge(5)

A:

Q: 4. Show that if x, y, z are integers such that x2 + y2 + z? = 2xyz, then x = y = z = 0. (H)

A:

Q: Prove that V2 is irrational.

A: We will prove by the method of contradiction. We will first assume the number to be rational and…

Q: Let V = {cities of Metro Manila} and E = {(x, y) |x and y are adjacent cities in Metro Manila}. %3!

A: Given: Let v= cities of Metro Manila  and E=x,y/ x and y adjacent cities in Metro Manila The…

Q: 4. Prove that, VR, -11-

A:

Q: U is a neighborhood of x0 and U ⊂ V, The V is a neighborhood of x0. (2) If U1 ...., U2 are…

A: Solution ::

Q: Prove that, if m | (a-b) then (a % m) = (b % m)

A: Since you have asked multiple questions we will solve the first question for you. If you want to be…

Q: Prove that if a, b E Z - {0}, then gcd(a, b) = gcd(a, -b)

A: soln:gcda,b=Greatest common divisor of a and bEvery integer that divides a and bsimultaneously will…

Q: Show that if AB={0}, then P(A)≤P(B).

A: Given that

Q: (4). Show that of X~UCO,!) as Y=-n-X)~ txponenkalla),

A: i) Uniform distribution : If X follows Uniform distribution over interval (a, b ) then cumulative…

Q: v. Let Ac S, prove that P(Ā) = 1- P(A)

A: Given that

Q: A study by Forbes indicated that the five most common words appearing in spam emails are shipping!,…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: Show that For all z € C, with z + 0, then: |z|?z=1 = z

A:

Q: 1. Prove or disprove that (pg)→r and p(q-r) are equivalent.

A:

Q: 7. Establish for A is m × n and B, C are n x p, that A(B+C) = AB + AC

A:

Q: Prove that if A C B then P(A) C P(B).

A: Proof:

Q: Suppose that X is a subset of Y, such that P(Y)>0. Is true or false that P(X|Y) is equal to…

A: It is given that X is a subset of Y This means that PX∩Y=PX...(i) The formula for PX|Y is given by:…

Q: 3. Prove or disprove: If a | (b + c), then either a |b or a | c. h of the follo

A: Since you have asked for question number 3 , we have solved it for you.

Q: If A and B are n × n and A + B is symmetric, then A and B are symmetric.  True or False...provide a…

A: If A and B are n × n and A + B is symmetric, then A and B are symmetric.

Q: Let A = {a, a, b, c} and B = {a, b, c}. Prove that A = B. Thus, the number of times an element is…

A: Given A={a,a,b,c} and B={a,b,c} we  have to show that A=B, for  this we will show that A⊂B and B⊂A…

Q: Suppose that AS B and x E A. Use the method of "proof by contrapositive" to show that if x e B ¥ C,…

A: Given that A⊆B and x∈A. Then, since A⊆B,  x∈B To show: x∉BYC, then x∈C.  Using contrapositive…

Q: prove that if a>4 then (a-2)^2>4

A:

Q: 4. Use a proof by contrapositive to prove that, for integers r and y: if a+y is odd, then exactly…

A: Here we use  Odd + Odd = Even Even +Even =Odd   Note:According to our guidelines we can solve only…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.