If A and B are independent, prove that B and the complement of A are independent.

Q: If A × B ={(p, q),(p, r), (m, q), (m, r)},     find A and B.

A: A will be the set of the first ordinates  And B is the set of the second ordinates

Q: If A and B are mutually exclusive (A ∩ B = ∅), are A and B always independent? If the answer is no,…

A: The two events are said to be mutually exclusive, if the two events do not occur together. The two…

Q: 50000 00012. [8] 2 [+] 剧 的条目 72 = 2 元 dx 衙路2跨小嶝小鸡小 1000 1

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Q: Prove that |ab|= |a | |b| for any numbers a and b.

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Q: Show that if A ⊂ B, then C – B ⊂ C – A.

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Q: The (i.j)-entry of (AB)' is the (j,i)-entry of AB, which is Oa1;b1j + a2;b2; + + anibnj .... O…

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

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Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

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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: Let a, b, q, r E Z and assume that a and b are not both zero and b and r are not both zero. Show…

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Q: Given and prove

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Q: Show that if a &gt; b, and a, b i= 0, then b- 1 &gt; a - 1, provided that a and b have the same…

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Q: Find a counterexample to show that each of the statements is false.

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Q: arguments

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Q: Let V4 = 4 V2 = V3 = -2 Pi -2 P2 2 2 and S = {v1, v2, V3, V4}. Determine whether pl and p2 are in…

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Q: (a) Use PhaseLines to investigate the bifurcation diagram for the differential equation dy dt =ay -…

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Q: (b) Let A and Bị be independent; similarly, let A and B2 be independent. Show that in this case, A…

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Q: Show that A × B ≠ B × A, when A and B are nonempty, unless A = B

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Q: a3 and b Let a₁ a2 Determine whether b can be written as a linear combination of a₁, 32, and a3. In…

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Q: If A ⊂ B, can A and B be independent under any circumstances? Explain

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Q: if| A - B | = | A + B | . prove that A is orthogonal on B

A: Given, A-B=A+B

Q: Suppose gcd(ab,c)=1. Prove that abc | d if, and only if ab | d and c | d.

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Q: find AB, BA, A +B, A - B, A, B, 5A, 3B. Observe that AB + BA. Show that (A - B)(A + B) # (A + B)(A –…

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Q: k of [Adj A], it -i 0 i

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Q: Let a = (1, 3, 8) and b = (7, 3, 4). Compute 5a + 7b

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Q: Let A={2,y,z} and B={3,x,z}. How many distinct elements are in (A×B)∩(B×A)

A: Given, A={2,y,z} B={3,x,z} How many distinct elements are in (A×B)∩(B×A) ?