Nested loop

[object Object],[object Object],[object Object],May 18, 2010 ॐ NEPAL COLLEGE OF INFORMATION TECHNOLOGY  _ _ _ _ _ _ _ _ _ _ _ _ 2001

[object Object],[object Object],[object Object],[object Object],[object Object],May 18, 2010

[object Object],[object Object],[object Object],[object Object],[object Object],May 18, 2010 ‘ n’ objects ‘ x’ values

[object Object],[object Object],[object Object],May 18, 2010

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],May 18, 2010

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],May 18, 2010

[object Object],[object Object],[object Object],[object Object],[object Object],May 18, 2010 Negation Equivalent Statement When Is Negation True? When False?  x P ( x )  x P ( x )  x  P ( x )  x  P ( x ) For every x , P ( x ) is false. There is an x for which P ( x ) is false. There is an x for which P ( x ) is true. P ( x ) is true for every x .

[object Object],[object Object],May 18, 2010 Statement When True? When False?  x  y P(x, y)  y  x P(x, y) P(x, y) is true for every pair x, y. There is a pair x, y for which P(x, y) is false.  x  y P(x, y) For every x there is a y for which P(x, y) is true. There is an x such that P(x, y) is false for all y.  x  y P(x, y) There is an x for which P(x, y) is true for all y. For every x there is a y for which P(x, y) is false.  x  y P(x, y)  y  x P(x, y) There is a pair x, y for which P(x, y) is true. P(x, y) is false for every pair x, y.

[object Object],[object Object],May 18, 2010

[object Object],[object Object],[object Object],[object Object],May 18, 2010

Nested loop

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