Let A = {-1, 2, 5, 8}, B = {0, 1, 3, 6, 7} and R be the relation ‘is one less than’ from A to B, then how many elements will R contain?a)2b)3c)5d)9Correct answer is option 'B'. Can you explain this answer?

Question

Let A = {-1, 2, 5, 8}, B = {0, 1, 3, 6, 7} and R be the relation &lsquo;is one less than&rsquo; from A to B, then how many elements will R contain?a)2b)3c)5d)9Correct answer is option 'B'. Can you explain this answer?

Answer

Given,
A = { - 1 , 2 , 5, 8} and
B = {0 ,1 ,3 ,6 ,7 }
R = { ( - 1 , 0 ) , (2,3), (5,6)}
(Since , R = A is one less than from B) Hence, total number of elements in R is 3.

Answer

Given,
A = { - 1 , 2 , 5, 8} and
B = {0 ,1 ,3 ,6 ,7 }
R = { ( - 1 , 0 ) , (2,3), (5,6)}
(Since , R = A is one less than from B) Hence, total number of elements in R is 3.

Answer

Explanation:

Given:
A = {-1, 2, 5, 8}
B = {0, 1, 3, 6, 7}
Relation R: 'is one less than'

Explanation:
To find the number of elements in the relation R, we need to determine which elements in set A are one less than the elements in set B.

Identifying elements in R:
- For element -1 in set A, there is no element in set B that is one less than it.
- For element 2 in set A, there is no element in set B that is one less than it.
- For element 5 in set A, there is only one element in set B that is one less than it, which is 6.
- For element 8 in set A, there are two elements in set B that are one less than it, which are 7 and 6.

Calculating the total number of elements in R:
Since there are a total of 3 elements in set A that have a corresponding element in set B such that the element in set B is one less than the element in set A, the relation R will contain 3 elements.
Therefore, the correct answer is option B) 3.

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