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SY Common ISE ODD 25-26

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Which of the following statements is/are TRUE for undirected graphs? 

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In an adjacency matrix blankA of an undirected graph, A not stretchy left square bracket i not stretchy right square bracket not stretchy left square bracket j not stretchy right square bracket equals 1 indicates:

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An isomorphism of graphs G and H is a bijection f the vertex sets of G and H. Such that any two vertices u and v of G are adjacent in G if and only if ____________

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Which of the following is a poset?
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If f and g are functions such that f∘g is onto, then:
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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 and relation R on A be Rblank equals not stretchy left curly bracket not stretchy left parenthesis a comma b not stretchy right parenthesis text end text straight ∣ text end text a minus b text  is divisible by 2 end text not stretchy right curly bracket. How many relations S on AA satisfy R subset of or equal to S subset of or equal to A cross times A?
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Which of the following posets forms a lattice?
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Use the Well-Ordering Principle to prove: “Every integer n > 1 has a prime divisor.”

Suppose you assume the contrary and let S be the set of counterexamples (integers >1 with no prime divisor), and let n be the least element of S.

Which of the following is the crucial next step that leads to a contradiction?

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Let domain be the set of non-negative integers. Is the statement ∀x ∃y (x < 2y) true? Give a witness y as function of x.
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