Let A, B, C be sets. Prove that if C ⊆A, then A −(B −C) = (A −B) ∪C. Analogously, for any real numbers a, b, and c, recall that a −(b −c) = (a −b) + c.

Q: If n(A) = 59, n(B) = 21, and n(A ∩ B) = 4, find n(A ∪ B).

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Q: If R is an integer domain, show that it contains exactly two elements a that satisfy a? = a.

A: Given R is an integral domain. We have to show that it contains exactly two elements a that satisfy…

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Q: Let a, b e R. Prove that if 15a + 206 = 49, then a and b are not both integers.

A: we have 15a+20b =49 and a and b both are in R  we prove that a and b are not both integers.

Q: Qing is twice as old as Rayna. Qing is 4 years younger than Paolo. The average age of Paolo, Qing…

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Q: Show that if a < c< b, then fave (a, b) = () fave l(a, c) + C - a | favg [c, b]

A: Solution...

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A: Consider the given equation. Find the characteristic for c if a, b are positive integers and ( x, y…

Q: Let a and d be integers. Prove that if d|(8a+7)and d|(5a+4), then d|3

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Q: = Let a, b, and d be positive integers. Prove that if (a, b) : divides a, then (d, b) = 1.

A: Definition of gcd (a, b) =1 is a and b does not have common prime divisor. Using this we can easily…

Q: Prove that a b + 2c + 3d + c+ 2d + 3a Let a, b, c, d be positive real numbers. C d + 2a + 3b + d a +…

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Q: Prove that if a,b belong R(Real Numbers) then |a|-|b| is lesser or equals to |a-b|

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Q: Prove: If (where b + 0 and d + 0), then C + d d a + b

A: Consider the given information, If ab=cd then show that a+bb=c+dd. First we consider ab=cd.

Q: Let a, b, c be three consecutive odd nubmers, with a < b < c. What is the  value of a2−2b2+c2?

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Q: Show that A x (B\C) = (A × B)\(A× C). Please do not use membership tables.

A: Given  A X (B\C) = (A X B)\(A X C)

Q: - BJ -1]. prove prove A²-A-51 = 0 3 If A =

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Q: Determine whether each funcuon is even, odd or neither. 1. fx)=x +x 2. fix)=+x 3. fr)=x-x 4.…

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Q: Let f(x) = Ax² + Bx + C where A, B and C are real numbers. Prove that if f(x) is an integer whenever…

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Q: Let a, b and c be integers. Prove that if a does not divide b and a|(b+c), then a does not divide c

A: Let a, b and c be integers.

Q: Determine whether the statement is true or false. Prove the statement directly from the definitions…

A: a. For all integers a,b, and c, if a | bc, then a | b or a | c.To demonstrate this assertion, we'll…

Q: If n(A) = 64, n(B) = 16, and n(A ∩ B) = 4, find n(A ∪ B).

A: Given, n(A) = 64, n(B) = 16, and n(A ∩ B) = 4   The objective is to find n(A ∪ B).

Q: Use proof by contradiction to show that no integers  y and z exist for which 24y + 12z = 1.

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Q: 2. For all sets X, Y and Z, determine whether each of the statement is true or false. If it is true,…

A: (a) False. We know that if a set A has cardinality n , then it's power set P(A) has cardinality 2n…

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Q: d = (a, b, c).

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Q: Suppose that x is a real number and that UCR. Prove that the following two conditions are…

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Q: Determine which of these relations are symmetric. The variables x, y represent integers. OxRy means…

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