Question 1010653
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(1) f and g are functions on X={1,2,3} as f—{(1,2); (2,3); (3,1)) ; g=(1,2);   (2,1); (3,3)}. Compute; fog and gof

(2) Let F, be the number of faces in G, where G is a connected planar simple graph with E edges and V vertices. Obtain an equation connecting F. E and V. Hence derive value(s) of F, E and V to form a graph such that the graph is a planar.

(3) Deduce the combination of n+1 element taken n-1 at a time denoted as C
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(2) F  - E + V = 1.

    Draw any planar graph on a plane and check this formula.
    It is the planar analog of the famous Euler's formula for the numbers of faces, edges and vertices of a polyhedron.


(3) {{{C[n+1]^(n-1)}}} = {{{((n+1)!)/((n-1)!*2!)}}}  = {{{((n+1)*n)/2}}}.

    See the lesson <A HREF=http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A> in this site.
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