Zero and one rules

Summary

\(a,b∈R\) :

• \(a+0=a\)
• \(a⋅1=a\)
• \(a⋅0=0, \)
• \(a⋅b=0\) i f and only if \(a=0\) or \(b=0\) (or both)
• \(a⋅b≠0\) i f and only if \(a≠0\) and \(b≠0\)
• If \(a≥0\) and \(b≥0\) then \(a⋅b≥0\)
• If \(a≤0\) and \(b≤0\) then \(a⋅b≥0\)
• If \(a≥0\) and \(b≤0\) then \(a⋅b≤0\)
• If \(a≤0\) and \(b≥0\) then \(a⋅b≤0\)