Inequality

If r > 0, then for all p and q such that pq does not equal 0 and such that pr > qr, we have:

  1. p > –q
  2. p > q
  3. 1 > q/p
  4. 1 < q/p
  5. none of these


Show/Hide Solution

Since r is not equal to 0, we can divide by r, and since r > 0 we know pr > qr implies p > q. We have three possibilities to consider, so let’s try specific values.

Note: p < 0 and q > 0 is impossible since p > q.

p q    p q    a    b    c    d
                 p > –q    p > q    1 > q/p    1 < q/p
+ +    6 3    F    F    T    F
+    6 -3    F    F    T    F
   -3 -6    F    T    F    T

Since none of the conditions (a), (b), (c), or (d) holds for every possibility of p and q, we conclude that (e) is the correct response.

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