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SY Common ISE ODD 25-26

SY Common ISE ODD 25-26

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The reflexive closure of

is:

R ∪ {(2,1)}

R ∪ {(3,3)}

R ∪ {(1,1), (2,2), (3,3)}

R ∪ {(1,3)}

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Let A be a 10-element set. How many ordered pairs (X,Y) of subsets satisfy X⊆Y and |Y|=6?

Let A, B, and C be subsets of a universal set U.

Suppose A ⊆ B and B ∩ C = ∅. Which of the following statements must be true?

Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex?

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Using strong induction to prove claims: which hypothesis allows proving for n+1?

Assume for n-1 only

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Assume true for all k with 1≤k≤n