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Logic basic

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Express each of the sentences using predicates , quantifier logical connectives and mathematical operations
where the domain consists of all integers

1) The product of 2 negative number is positive

2) The average  of 2 positive integers is positive

3) The difference of 2 negative numbers is not neccesarily negative

4) The absolute value of the sum of integers does not exceed The sum of the absolute values of these integers

1 Answer

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Please cehck and point out my mistakes :)

1) The product of 2 negative number is positive :

∀x∀y(x<0 ∧ y<0 --->(xy>0))

2) The average of 2 positive integer is positive

∀x∀y(x>0 ⋀ y >0 --->(x+y)/2 >0 )

3) The difference of 2 negative numbers is not necesarily negative

∼∀x∀y(x<0 ⋀ y<0 --->(x-y)<0))

4) The absolute value of the sum of integers does not exceed The sum of the absolute values of these integers

: ∀x∀y(Abs(x+y) ≯ (Abs(x)+Abs(y)))
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