B\ Prove that if T is a spanning tree of G which contains e, then Te Is a spanning tree of G * e.
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- 5. Determine whether the relation with the directed graph is an equivalence relation:Can you carefully explain part C please? You don't need to do B I just thought you need it for part C..Let T be a rooted tree that contains vertices u, v, and w (among possibly others). Prove that if w is a descendant of both u and v, then u is a descendant of v or v is a descendant of u.
- Let G be a simple graph. Show that the relation R on the set of vertices of G such that uru if and only if there is an edge associated to {u, v} is a symmetric, irreflexive relation on G.Let N (A) A = = span 4 5 -6 -2 -2 6 2 -4 - 10 –7 6 2 Find a spanning set for the null space of A. -4 4 - 3 18 51Question Number 07 a) Determine whether the relation with the directed graph shown is an equivalence relation. b) Determine whether the relation represented by the zero-one matrix is a poset (partial order set): [1 1 1] Lo 1.