Section IV.1
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Problem IV.1.1
Draw three crosses and four noughts.
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(a)
How should the arrows go from the crosses to the noughts so that a map of the set of crosses into the set of noughts is obtained? Suppose the arrows define a map.
(b)
Can they be drawn so that every image has a unique preimage?
(c)
Can they be drawn so that every nought has a preimage?
(d)
Answer the same questions if there are four crosses and three noughts.
(e)
For what number of noughts is a one-to-one map of a set of three crosses possible?
Problem IV.1.2
Let the transformations , and have inverses. Find the transformation inverse to their product .
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Problem IV.1.3
Write the formulas defining the axial symmetry about the line having the equation in a Cartesian rectangular coordinate system.
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