Consider the set of all-Natural numbers and a relation R defined on the set, containing all ordered pairs of the form (a, b) only when a divides b. Then which of the following pairs is a pair of elements that are not comparable?
0 (4,32)
0 (7,28)
0 (3,25)
0 (8,16)
Answers
Answer:
3
Explanation:
3 and any subsequent wordswas ignored because we limit queries to 32 words
Answer:
The pair of elements that are not comparable: The correct answer is (7,28)
Explanation:
In a partially ordered set, two elements a and b are said to be comparable if either a ≤ b or b ≤ a, otherwise, they are not comparable.
In the given relation R, an element a is said to divide another element b if and only if b is a multiple of a. Therefore, the relation R is a partial order on the set of natural numbers.
Now, we need to check whether each of the given pairs is comparable or not.
(4, 32) : Here, 4 divides 32, so (4, 32) ∈ R, and hence 4 ≤ 32. Therefore, this pair is comparable.
(7, 28) : Here, 7 does not divide 28, so (7, 28) ∉ R. Also, 28 does not divide 7, so (28, 7) ∉ R.
Therefore, 7 and 28 are not comparable.
(3, 25) : Here, 3 does not divide 25, so (3, 25) ∉ R. Also, 25 does not divide 3, so (25, 3) ∉ R. Therefore, 3 and 25 are not comparable.
(8, 16) : Here, 8 divides 16, so (8, 16) ∈ R, and hence 8 ≤ 16. Therefore, this pair is comparable.
Hence, the pair of elements that are not comparable is (7, 28).
For more such question: https://brainly.in/question/23828537
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