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

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

Options:

Correct Answer: 6

Solution:

The 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 = {(a, b) | a < b}. How many ordered pairs are in R?

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

Step 1: Identify the set A, which is {1, 2, 3, 4}.
Step 2: Understand the relation R defined by R = {(a, b) | a < b}. This means we are looking for pairs (a, b) where the first number is less than the second number.
Step 3: List all possible pairs (a, b) from set A where a < b.
Step 4: Start with the smallest number in A, which is 1. The pairs with 1 are (1, 2), (1, 3), and (1, 4).
Step 5: Move to the next number, which is 2. The pairs with 2 are (2, 3) and (2, 4).
Step 6: Next, take the number 3. The only pair with 3 is (3, 4).
Step 7: Now, list all the pairs we 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 in total.

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