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Determine whether each of the following statements is TRUE or FALSE. Justify your answers. a. Let A = {1,2} and B = {a,b,c). Relation R={(1,a),(2,5),(2,c)} is a function The range of S = {(1,x),(2,y),(3,x),(4,x)} is {x,y). b. c. Let / be a function from X to Y. Then we say that is everywhere defined if Ran (S) = X d. Let g be a function from X to Y. Then g is injective if and only if VX, X, X, g(x) = g(x) → X; = Xz. e. f. g. Let h be a function from X to Y. Then h is bijective if and only if h is either injective or surjective. A graph is called simple if it does not have any loops or parallel edges. A graph H is said to be a subgraph of a graph G if and only if every vertex of His also a vertex in G, every edge in H is also an edge in G and every edge in H has the same endpoints as in G. An edge is a bridge in a connected graph G if deleting it will create a disconnected graph. A path is defined as a closed trail. If a graph has more than one vertex of odd degree, then it cannot have an Euler path. h. i. 1. [20 marks]