Question

Let A={18,25,5,30}. List the ordered pairs in the relation R={(a,b)∈A×A, a

Answer 1

The ordered pairs that form the relation R where a is less than b (a < b) from the set A={18,25,5,30} are (5,18), (5,25), (5,30), (18,25), (18,30), and (25,30).

Step-by-step explanation:

The set A given in the question is A={18,25,5,30}. We are asked to list the ordered pairs in the relation R consisting of all pairs (a,b) such that both a and b are elements of A, and a is less than b (a < b).

To find the relation R, we compare each element in A with every other element to determine if the first element is less than the second. The ordered pairs that satisfy this condition will be part of the relation R.

Let's create the relation R by comparing elements:

• (5,18) since 5 < 18
• (5,25) since 5 < 25
• (5,30) since 5 < 30
• (18,25) since 18 < 25
• (18,30) since 18 < 30
• (25,30) since 25 < 30

Thus, the complete set of ordered pairs for the relation R is:

• (5,18)
• (5,25)
• (5,30)
• (18,25)
• (18,30)
• (25,30)

Answer 2

The relation R is defined on set A={18, 25, 5, 30}, where R={(a, b)∈A×A, a<b}. Examining each element, we find (25,30) as 25 is followed by 30. For 5, the pairs are (5,18) and (5,30). No pairs involve 18 or 30. Thus, R={(25,30), (5,18), (5,30)}.

Step-by-step explanation:

In the relation R defined on set A={18, 25, 5, 30}, where R={(a, b)∈A×A, a<b}, we identify ordered pairs by ensuring the first element is less than the second.

For 18, no elements exceed 18, yielding no pairs. For 25, the only element greater is 30, resulting in the ordered pair (25,30).

Considering 5, where 18 and 30 are greater, we obtain the pairs (5,18) and (5,30). For 30, no elements surpass it, leading to no pairs.

Thus, the ordered pairs in R are (25,30), (5,18), and (5,30), reflecting the relations where the first element is less than the second in set A.

Let A={18,25,5,30}. List the ordered pairs in the relation R={(a,b)∈A×A, a<b}. R={}.