Question

Prove that a tree with n node has exactly n-1 edges. Please show all steps. If it connects to Induction that works too.

Answer #1

A binary tree isfullif every non-leaf node has exactly two
children. For context, recallthat we saw in lecture that a binary
tree of heighthcan have at most 2h+1−1 nodes, and thatit achieves
this maximum if it iscomplete, meaning that it is full and all
leaves are at the samedistance from the root. Findμ(h),
theminimumnumber of nodes that a full tree of heighthcan have, and
prove your answer using ordinary induction onh. Note that tree of
height of 0 isa single...

can you please show all the steps thank you...
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Show all steps in your proof. Use handshaking theorem

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Prove by induction that 3n < 2n for all
n ≥ ______. (You should figure out what number goes in the
blank.)

In lecture, we proved that any tree with n vertices must have n
− 1 edges. Here, you will prove the converse of this statement.
Prove that if G = (V, E) is a connected graph such that |E| =
|V| − 1, then G is a tree.

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please solve it step by step. thanks
Prove that every connected graph with n vertices has at least
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n)

Please show all the steps..thankyou
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Prove that a simple graph with p vertices and q edges is complete
(has all possible edges) if and only if q=p(p-1)/2.
please prove it step by step. thanks

Show all the steps and explain. Don't skip steps and please
clear hand written
f(x)=x^m sin(1/x^n) if
x is not equal 0 and f(x)=0 if x =0
(a) prove that when
m>1+n, then the derivative of f is continuous at 0
limit x to 0 x^n
sin(1/x^n) does not exist? but why??? please explain it should be
0*sin(1/x^n)

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