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Example 4 If :formula: form the set Solution We have, Px PxP= {(1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2), (2,2,1), Example 5 If :formula: is the set of all real numbers, what do the cartesian products and :formula: represent? Solution The Cartesian product :formula: represents the set R × R={(x, y) : x, which represents the coordinates of all the points in two dimensional space and the cartesian product :formula: represents the set which represents the coordinates of all the points in three-dimensional space. Example 6 If :formula: :formula: :formula: find :formula: and Solution EXERCISE 2.1

  1. If find the values of and
  2. If the set :formula: has 3 elements and the set :formula: then find the number of elements in
  3. If :formula: and :formula: find :formula: and
  4. State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly. (i) If :formula: and :formula: then (ii) If :formula: and :formula: are non-empty sets, then :formula: is a non-empty set of ordered pairs :formula: such that :formula: and (iii) If :formula: :formula: then
  5. If :formula: find
  6. If :formula: Find :formula: and
  7. Let :formula: :formula: :formula: and :formula: Verify that (i) :formula: (ii) :formula: is a subset of
  8. Let :formula: and :formula: Write :formula: How many subsets will :formula: have? List them.
  9. Let :formula: and :formula: be two sets such that :formula: and :formula: If are in :formula: find :formula: and :formula: where :formula: :formula: and :formula: are distinct elements.

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