The domain of discourse is Z= integers..are the following statements true of fal

Question

The domain of discourse is Z= integers..are the following statements true of false.. 1. For all x in Z there exists some y, such that the absolute value of x > y ....... i will write it as [x]>y 2. there exists a y in Z for all x in z, [x]>y 3. for all x in z ( [x] <0) ---> (17=0) ) 4. there exists an x in z (( [x] <0) or (17 is not equal to 0) ) please explain the true or false answers...Thanks

Explanation / Answer

1.True. If x is negative, y can be x itself. [x] >x. If x is positive, y can be -x. 2.False. Consider y=x+1. [x+1]>x always. 3. True. [x] is never less than 0. So, the statement is vacuously true. 4. True. [x]

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