A student claims that for every relation the range and codomain are the same. Examine this statement in the context of the relation described below and answer the questions.
a. (i) Explain, without using numerical examples, the conceptual difference between the range and the codomain of a relation.
b. (ii) The sets P={2,4,6,8} and Q={1,2,3,4,5,6} are given. A relation R⊆P×Q is defined by R={(2,3),(4,3),(6,5)}. Determine the domain, codomain and range of R.
c. (iii) Using your answer to part (ii), state whether the student’s claim is true for this relation. Justify your answer in one or two sentences.