Can Basic Algebra Prove These Mathematical Statements?

[shanshayan]

please proof​

1) a.0=0
2) a^2≥0
3) -1/a=1/-a
4) a-(b-c)=(a-b)+c
5) if a.b=o a=0 or b=0
6) if a≤x≤b and a≤y≤b then |x-y|≤b-a

​

 

[Fredrik]

please proof​

1) a.0=0
2) a^2≥0
3) -1/a=1/-a
4) a-(b-c)=(a-b)+c
5) if a.b=o a=0 or b=0
6) if a≤x≤b and a≤y≤b then |x-y|≤b-a

​

You need to show us your own attempt to solve these problems. If you have no idea how to solve them, it's OK to just say that, but then you still have to give us more information. In particular, you need to tell us if these variables represent real numbers, vectors, or something else. You also need to tell us what information from your book you're allowed to use. Does the problem say that these statements are all true, or are you supposed to determine which ones that are? Number 4 looks wrong, but maybe the + sign is supposed to be -. Does a period (.) denote multiplication of real numbers, or is it the dot product of vectors? Are these statements about three specific real numbers a,b,c, or are they supposed to be statements about all real numbers? For example, is number 2 supposed to say "For all real numbers a, a²≥0", or is a some specific real number that you've been given (like -3), and you're supposed to prove that its square is ≥0?

 

[HallsofIvy]

Looks like homework to me.

 

[mtayab1994]

please proof​

1) a.0=0
2) a^2≥0
3) -1/a=1/-a
4) a-(b-c)=(a-b)+c
5) if a.b=o a=0 or b=0
6) if a≤x≤b and a≤y≤b then |x-y|≤b-a

​

These proofs are so simple all you have to use to prove them is want you learned in general mathematics preferably algebra.