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SY Common ISE ODD 25-26

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Who first solved the Königsberg Bridge Problem?

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Consider the given graph

 Its Minimum cost spanning tree is ___

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Let A equals not stretchy left curly bracket 1 comma 2 comma 3 comma 4 not stretchy right curly bracket. Define a relation R subset of or equal to A cross times A such that (ablank comma b not stretchy right parenthesis element of R iff a plus b is even.

How many

equivalence classes does R have?
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Which of the following relations on integer numbersZ is not transitive?

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The relation Error converting from MathML to accessible text. on integers is:
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If f not stretchy left parenthesis x not stretchy right parenthesis equals 2 x plus 3 and g not stretchy left parenthesis x not stretchy right parenthesis equals x squared, then not stretchy left parenthesis f ring operator g not stretchy right parenthesis not stretchy left parenthesis x not stretchy right parenthesis equals not stretchy ?
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Consider lattice of divisibility on {1,2,4,8,16}. What is join(4,8) and meet(4,8)?
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Determine status of ∃x ∀y (R(x) ∨ ¬R(y)) over nonempty domain.
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In the Hasse diagram of divisibility on {1,2,4,8}, the number of edges = ?
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The function f colon natural numbers rightwards arrow natural numbers defined recursively as fblank not stretchy left parenthesis 0 not stretchy right parenthesis equals 1 comma text   end text f not stretchy left parenthesis n plus 1 not stretchy right parenthesis equals 2 f not stretchy left parenthesis n not stretchy right parenthesis. What is f(5)?
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