Problem 39E
Explain why A × B × C and (A × B) × C are not the same.
Step-by-Step Solution:
Solution:Step 1:We have to explain why A × B × C and (A × B) × C are not the same.Step 2: We know the cartesian product is not associative. Suppose A={x,y,z} ,B={1,2,3} and c={a,b}AXBXC={(x,1,a),(x,2,a),(x,3,a),.........} ..................(1)Now AXB={(x,1),(x,2),(x,3),(y,1),(y,2).....}(AXB)XC={((x,1),a),((x,2),b),((x,3),a).......} ..............(2)Therefore, AXBXC(AXB)XC
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