The defining property of an ordered pair is that two or- dered pairs are equal if and only if their first elements are equal and their second elements are equal. Surprisingly, instead of taking the ordered pair as a primitive con- cept, we can construct ordered pairs using basic notions from set theory. Show that if we define the ordered pair (a, b) to be {{a}, {a, b}}, then (a, b) = (c, d) if and only if a = c and b = d. [Hint: First show that {{a}, {a, b}} = {{c}, {c, d}} if and only if a = c and b = d.]
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.
Hi! I am having some trouble with this one task. It is from "discrete mathematics and its applications 8th edition". The task is number 49, from chapter 2.1 page 133. I have added a screenshot of the task aswell.
![* 49. The defining property of an ordered pair is that two or-
dered pairs are equal if and only if their first elements are
equal and their second elements are equal. Surprisingly,
instead of taking the ordered pair as a primitive con-
cept, we can construct ordered pairs using basic notions
from set theory. Show that if we define the ordered pair
(a, b) to be {{a}, {a, b}}, then (a, b) = (c, d) if and only
if a = c and b = d. [Hint: First show that {{a}, {a, b}}
{{c}, {c, d}} if and only if a = c and b = d.]
:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9625243a-f3bb-4541-a941-227023287162%2Fdabba1b4-bde0-4ae2-8fd3-4442c2808cc6%2F7uzcdds_processed.png&w=3840&q=75)
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