Example 2.42. Showing sets are equal. Consider the following two sets: A (eQthe decimal expansion of a has at most two digits to the right of the decimal place} B= (x€Q| 100.r e Z). Show that A=B. Proof: How many statements do we need to prove? What are they?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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![Example 2.42. Shourng sets are equal. Consider the following two sets:
A-(reQthe decimal
expansion of ar has at most two digits to the right of the decimal place}
B= {z €Q] 100.r e Z).
Show that A=B.
Proof: How many statements do we necd to prove? What are they?
Proof that A is a subset of B: Start with x in the set A. What do you know about x?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d940ce8-cba2-4a95-af25-aae0739ca5aa%2F705b16bc-eedb-4373-8ebd-fd32b94bbe66%2Fya6y19_processed.jpeg&w=3840&q=75)
Given
To prove
Let us consider an arbitrary element
Then has any of the following forms
Where are integers.
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