The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of every watermelon to the nearest pound. The number of pounds read off the scale for each watermelon is called its measured weight. The domain for each of the following relations below is the set of watermelons on the truck. For each relation, indicate whether the relation is: • Reflexive, anti-reflexive, or neither • Symmetric, anti-symmetric, or neither • Transitive or not transitive Justify your answer. (a) Watermelon x is related to watermelon y if the measured weight of watermelon x is at least the measured weight of watermelon y. No two watermelons have the same measured weight. (b) Watermelon x is related to watermelon y if the measured weight of watermelon x is at least the measured weight of watermelon y. All watermelons have exactly the same measured weight.
The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of every watermelon to the nearest pound. The number of pounds read off the scale for each watermelon is called its measured weight. The domain for each of the following relations below is the set of watermelons on the truck. For each relation, indicate whether the relation is:
• Reflexive, anti-reflexive, or neither • Symmetric, anti-symmetric, or neither • Transitive or not transitive Justify your answer.
(a) Watermelon x is related to watermelon y if the measured weight of watermelon x is at least the measured weight of watermelon y. No two watermelons have the same measured weight.
(b) Watermelon x is related to watermelon y if the measured weight of watermelon x is at least the measured weight of watermelon y. All watermelons have exactly the same measured weight.
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