(2c) Prove or disprove the following statement: “ A UBCANB for any A and B "

Q: How would you write a formal proof for if AnB = B then B is a subset of A?

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Q: Construct a proof that ZEIF = ZGIH. н

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Q: Exercise 4.4.7. Let n be odd. Prove that if we divide n² by 8, then the remainder is always 1.…

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Q: (a) Suppose we're interested detecting whether there is a significant difference in the duration of…

A: Introduction Hypothesis is an assumption that is being tested.

Q: c. sin"(t)- cos (t) = 2sin (t)-1 = CS d. cot (2y)+cos?(2y)+ sin (2y) = csc²(2y)

A: Given,  c. sin4(t)-cos4(t)=2sin2(t)-1d. cot2(2y)+cos2(2y)+sin2(2y)=csc2(2y)

Q: Use Definition 1.1.4 to prove that {x:|x| 0, and -x if x < 0.

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Q: iii. P(AN B) = P(A) N P(B). iv. P(A) UP(B) C P(AUB)

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Q: Prove the following statement: [a 0 0 If A = 0 b 0 ,a + 0, b + 0, c + 0, 0 |.a + 0, b + 0, c + 0,…

A: To prove: If A=a000b000c, a≠0, b≠0, c≠0, then A-1=1a0001b0001c.

Q: Given f (x) 4x2 - 3x + 2 and g(x) = 3x + 1 Find the following: Part a: f(x) + g(x) Part b: f(x) –…

A: Sum and difference of the functions

Q: 55. y = aln «

A: As per our guidelines, we are allowed to answer the first question please resubmit the other…

Q: Prove: If = ¿ (where a, b, c, and d are nonzero), b then d*

A: Given:               ab=cd  (where a,b,c  and d are non zero.)

Q: п(5n-1) 2 + 7+ 12 + …+ (5n – 3) = ... - 2

A: We will prove the game statement by using the principle of mathematical induction in which we show…

Q: - 3 - 3 - 8 Let v1 = 0 |. v2 = V3 = Determine if u is in Nul A, where A = V1 v2 V3 and u 8 10 5 8 Is…

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Q: vx (P(x) → (Q(x) v R(x))), – 3x (P(x) ^ R(x)) | vx (P(x) → Q(x))

A: To prove the validity of the following: ∀x(P(x)→(Q(x)∨R(x))), ¬∃x(P(x)∧R(x))⊢∀x(P(x)→Q(x))

Q: 4c Let m and n be integers. If m +n is even, then either ma even or m and n are both odd. 10 = 2F+1…

A: Consider the following statement: For all integers m and n, if m+n is even then m and n are both…

Q: Identify the axiom or postulate that applies to the following statement.     If m = n, then m – z =…

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Q: b) Convert the binary numbers 1110011110101001 to it hexadecimal equivalent?

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Q: Differentiate: f(x) = 4x³ - (5/x²) %3D O a. f(x) = 12x2 - (10/x³) O b. f(x) = 12x2+ (10/x³) O c.…

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Q: 3. Let n e Z be nonzero and even. Prove that there exist unique a € {0, 1}, b € N, and odd c€ N such…

A: Since n is even and non-zero . Since n is non zero ⇒ n is either positive or negative. Let's write…

Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A (A)° = A - int A %3D…

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

Q: . Show that sup{3 – 2 : n = 1,2, ...} = 3. %3D

A:

Q: a, be R H I 's an ideal of R if and anly of a-beI. for then a+I b+I %3D

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Q: -1 -2 -3 -4- 1 2 Let A = 1 1-

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Q: If x ER, x > 0 and r, s are rational numbers, then (i) x > 0; (ii) for x > 1, x" <xs if r < s

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Q: Let a, b, and p be positive integers. (a) Prove that if pjab ) (pja or pjb), then p = ab ) (p = a…

A: let a,b,p be positive integers. (a) to prove that if p|ab⇒p|a or p|b then p=ab⇒p=a or p=b as given…

Q: (b) Prove that E-o(-1)* )= 0 for all positive integers m.

A: We have to prove ∑k=0n-1kkn=0 for all positive integer n

Q: Use De Morgan’s Laws to determine whether the two statements are equivalent           ~ (p Λ q),…

A: Recall the De Morgan's Law as follows. ~A∨B≡~A∧~B~A∧B≡~A∨~B

Q: Adjusted R R Square R Square .801 .641 564 a. Predictors: (Constant), X6, X5, X4, X3, X2, X1 Model…

A: The output provides information about a multiple linear regression model with six predictor…

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

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Q: Choose an n and m that satisfies the following statement

A: We need an example such that  n = m! Take n = 24 and m = 4  Then m! = 4! = 24 Hence , n = m!