Let A = {1, 2, 3, 4} and R be the relation defined by R = {(x, y) | x < y}. H

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Question: Let A = {1, 2, 3, 4} and R be the relation defined by R = {(x, y) | x < y}. How many ordered pairs are in R?

Options:

Correct Answer: 6

Solution:

The ordered pairs are (1,2), (1,3), (1,4), (2,3), (2,4), (3,4). Thus, there are 6 ordered pairs.

Let A = {1, 2, 3, 4} and R be the relation defined by R = {(x, y) | x < y}. How many ordered pairs are in R?

Let A = {1, 2, 3, 4} and R be the relation defined by R = {(x, y) | x < y}. How many ordered pairs are in R?

Step 1: Identify the set A, which contains the numbers {1, 2, 3, 4}.
Step 2: Understand the relation R, which consists of ordered pairs (x, y) where x is less than y (x < y).
Step 3: List all possible pairs (x, y) from set A where x < y.
Step 4: Start with the smallest number in A, which is 1. Pair it with all larger numbers: (1, 2), (1, 3), (1, 4).
Step 5: Move to the next number, which is 2. Pair it with larger numbers: (2, 3), (2, 4).
Step 6: Next, take the number 3. Pair it with the only larger number: (3, 4).
Step 7: Now, list all the pairs you found: (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4).
Step 8: Count the total number of pairs listed. There are 6 pairs.

Relations and Ordered Pairs – Understanding how to define and count ordered pairs based on a given relation.
Set Theory – Applying set theory to determine the number of valid pairs from a defined set.
Inequalities – Using inequalities to establish the conditions for forming ordered pairs.