Let A = {c, d, f, g), B = {f, j}, and C = (d, g}. CsA A) True (B) False

Q: Prove that if A ⊂ B and B ⊂ C, then A ⊂ C

A: Given problem is :   Prove that if A ⊂ B and B ⊂ C, then A ⊂ C.

Q: Let A, B and C be members of C. Compare An (BuC) and (An B)U(AnC)

A: A Venn diagram is a graphical representation of a sample space. The sample space in a Venn diagram…

Q: Let U = {h, i, j, k, I, m, n, o, p} A = {h, i, j, m} B= {h, k, I, m, o}

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

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Q: 8. Let A = {Al, Beth}and B = {up, down, left, right}. Fine %3D

A: # we are entitled to solve one question at a time, please resubmit the other questions if you wish…

Q: (b) Let {Ai e I}. Prove that 4) =UA;. |A, iel

A: We need to prove that ∩i∈IAic=∪i∈IAic  for set Ai/i∈I We will prove using the following method: To…

Q: Let V = { a, e, i, o, u } andB = { a, i, k, u}. Find V – B and B – V

A: V-B= elements those lie in V but not in B  Hence, V-B={e,o}

Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

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Q: Give a natural deduction proof of ¬(A V B) from hypothesis ¬A A¬B.

A: Please find the answer in next step

Q: Let S = { a, {1, b} , (2 , c),4}, then {1, b} e S O TRUE O FALSE

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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}

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Q: Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that(i) A × (B ∩ C) = (A ×…

A: i) Answer(i) A × (B ∩ C) = (A × B) ∩ (A × C) (proved)

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

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Q: Re(z,€,) = Re(*,)R (z,) O True O False

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Q: and they are independent

A: *Answer:

Q: Let A, B and C be members of C. Compare An(BUC) and (An B) U (AnC)

A: Introduction: Suppose x belongs to the set A ∩ (B ∪ C).

Q: If all fruit bearing plants are flowering plants, and all flowering plants attracti nsects. Which of…

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Q: Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and    B = {3, 4, 5}. Find A′, B′ , A′ ∩ B′, A ∪ B and hence…

A: Given: Now, The set of all those elements of U which do not belongs to A is called the complement…

Q: Show that QQ(2^1/4) is not normal. Further show that Q is subset of Q(2^1/2) and Q(2^1/2) is subset…

A: The objective is to show that Q214 is not normal. Further show that Q is subset of Q212 and Q212 is…

Q: Are na V Independen O No, f(u,v) + fulu)fy(v) O Yes, f(u,v) = fulu)fy(v) No, f(u,v) = fu(u)fy(v) O…

A: It is given that f(u,v)=4uv.

Q: Prove logically that " C, + "C, + "C, + …· +"C, = 2".

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Q: Let A = {c, d, f, g), B = {f, j}, and C = {d, g). BcA A True B) False

A: topic - sets

Q: Prove that if a|b and b|c, then a|c.

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Q: X and  Y are randam variables then XeY is a randam variables.

A: Here, The X and Y are two random variables  Then XeY are also random variables we have to show Here…

Q: nce, a, provided then what conclusion

A: P value is the probability value calculated under the test statistic

Q: السؤال 13 If S is a subset of T, then u*(T) sµ* (S). 0 صواب ihi O

A: I will use the definition of measure to answer this question.

Q: 3. Prove: a) Bo(U,4,)=U,(BO4) b) BU(N,4)=N,(BU4)

A: a) B∩∪iAi=∪iB∩Aib) B∪∩iAi=∩iB∪Ai

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: Let A = a22 Show that if d = a¡|a» – A2jɑ12 # 0, then 1 A- = a22 -a12

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Q: Let U = a deck of cards and R = all the red cards and F = all the face cards, %3D then the queen of…

A: True.

Q: 7. Show that (a). (Z, +) # (Q, +). (b). (Q,+)# (Q\{0},.). (c). (R\{0},-) # (Q\{0},.). (d). (R\{0},-)…

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Q: If X, then Y. If Y, then Z, y is true, So:

A:

Q: o Let A-

A: The given matrix is : A=1-111 Calculate the value of norm A∞. We know the formula of the infinity…

Q: If A and B are independent, then

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Q: Prove that rem(ab,c) = rem(rem(a,c)rem(b,c),c)

A: Consider the given information. The term rem is defined as, rem(a, b) is the remainder when a is…

Q: 3 it is kno ity P(A U

A:

Q: Let a, b,c € R4. Prove that c+a a+b b+c c+b a +c b+a Al

A: a,b,c∈ℝ+ab+bc+ca≥c+ac+b+a+ba+c+b+cb+a

Q: If w is FALSE, x is TRUE, and y is FALSE, what is ((w OR y') AND (x' AND y')') OR ((w OR y')' AND (x…

A: If w is FALSE, x is TRUE, and y is FALSE, we need to find ((w OR y') AND (x' AND y')') OR ((w OR…

Q: 2) Let mf lu and (a,m)=| a,bE Z such that Let h= Om ( a) show and and (h,m)=1, %3D let. ne OmCab)…

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Q: Prove/Disprove: (¬A → ¬B) ® (¬C ^ A) = ¬(A v ¬B) → ¬(B –→ C)

A: Any two propositions are said to be equivalent if the truth value in each row of the truth table is…

Q: Let A = { c, d, f, g} B = { f, j} C= { d, g} Is C C C? True False

A: Every  set is subset  of it self Here C is subset  of C

Q: Prove rem (a+b,c) = [rem(a,c) + rem(b,c)] , c

A: Note: rema,b=the remainder when a is divided by b. Then, by the quotient remainder theorem, there…

Q: How to solve this?

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Q: Let A = (C, d, f, g}, B = {f, j}, and C = {d, g). Cc C A True B False

A: A set is a well-defined collection of objects, these objects are called the elements of the sets.…

Q: If u + v = u + w, then v = W. Select one: True False

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Q: The statment QV ~Q is always true

A: the given statement is Q∨~Q make a truth table as follows  Q ~Q Q∨~Q T F T F T T…

Q: 2. Let A = {0, 1, а, b, 8, 10, с, — 4}, В 3D {3, 1, 9, e, а, с, 0}, and С %3D {2, с, 10, 9, 8, —4,…

A: Using the definition of intersection, union and difference between two set

Q: Let U = {q, r, s, t, u, v, w, x, y, z} A = (q, s, u, w, y} B = (q, s, y, z} C= (v, w, x, y, z}…

A: Topic:-  set and sub set