Question
Suppose $a, b, c$, and $d$ are real numbers, $0<a<b$, and $d>0$. Prove that if $a c \geq b d$ then $c>d$.
Step 1
We want to prove that $c > d$. Since $0 < a < b$, we can divide both sides of the inequality $ac \geq bd$ by $b$ to get $\frac{a}{b}c \geq d$. Since $\frac{a}{b} < 1$ (because $a < b$), we can multiply both sides of the inequality $\frac{a}{b}c \geq d$ by Show more…
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The Language Of Logic
Proof Methods
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