1. Use a proof by contradiction to prove the following. (a) If m and n are integers such that m² is odd and m + n is even, then n is odd. (b) No integers x and y exist such that 4x² − 6y² + 1 = 8.

Q: If n(A ∪ B) = 97 and n(A) = n(B) = 61, find n(A ∩ B).

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Q: Find 4-¹, if A = [3 3 O ] 3 -2 0 O [32] −3 0 - [²2] O −3 12 -=[ 132] -3-2 O 2 3 3 2

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Q: If n(A ∪ B) = 50, n(A ∩ B) = 10, and n(B) = 20,find n(A).

A: Given,n(A∪B)=50,n(A∩B)=10 and n(B)=20 To find: n(A) Solution: We know,…

Q: From the list below, select the values of x for which f'(x) > 0. 2 -1 None of the listed x values -3…

A: Given graph of function

Q: verify that A + B = B + A

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Q: Write out the equation for the given graph: y =

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Q: 2+5+8+11+...293

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Q: If n(A ∪ B) = 97 and n(A) = n(B) = 66 find n(A ∩ B).

A: Given, n(A ∪ B) = 97 and n(A) = n(B) = 66

Q: The Honolulu Advertiser stated that in Honolulu there was an average of 667 burglaries per 300000…

A: It is expected to calculate probability that, P(r≥3) The formula for the probability distribution of…

Q: Which is the right option?

A: Pascal's identity states that Ckn=Ckn-1+Ck-1n-1 for any positive k and n. here  Ckn  are binary…

Q: X2-2x -6=0 of

A: Note:- according to the company policy we can attempt only one question so please upload the next…

Q: In a class that has 25 students, suppose that 24 of them took their exam on a Monday and the average…

A: Refer to the solution

Q: If n(A ∪ B) = 99 and n(A) = n(B) = 69, find n(A ∩ B).

A: Given, n(A ∪ B) = 99 and n(A) = n(B) = 69   The objective is to find  n(A ∩ B).

Q: So which one should I choose?

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: -7 -6 -5 -4 4 3 2 1 -1 -2 -3 -4 1 2 3 4 5 6

A: To find the rang by the given graph.

Q: The table shows the movement of a stock for 30 randomly selected trading days. "Up" means the stock…

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Q: It is wrong. It says they are both incorrect.

A: X-intercepts are found by substituting y=0 in the given function.

Q: D) lim f(x)=| 23 E) lim → 8 f(x) = F) lim f(x)= z 2

A: D) we know that, limx→3f(x)=limx→3+f(x)=limx→3-f(x)But limx→3+f(x)=2limx→3-f(x)=-1Since…

Q: If A = A-1 = -5 15 4 -11 -1 3 14 -12, then 3

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Q: -1 1 0 0 1 2 3 and B = 0 2 A = -3 1 A + B

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Q: 1 -3 -27 A =| -2 7 -2 5. 54

A: The given matrix is: A=1-3-2-275-254 Find the inverse of the matrix: Formula: A-1=1AAdj A, where Adj…

Q: If n(A ∪ B) = 99 and n(A) = n(B) = 65, find n(A ∩ B).

A: n(AUB) =n(A) +n(B) -n(A intersection B)

Q: Determine the nullity of 3 A = -2 1 -2 4

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Q: Dsery? 2.

A: