Question 14 of 33intermediate🔧 ApplyShort Answer3 marks

Let A={1,2,3,4,6}A = \{1, 2, 3, 4, 6\}. Let RR be the relation on AA defined by {(a,b):a,b∈A,b is exactly divisible by a}\{(a, b) : a, b \in A, b \text{ is exactly divisible by } a\}.

(i)

Write RR in roster form

Answer

R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (6, 6)}

(ii)

Find the domain of RR

Answer

Domain of R = {1, 2, 3, 4, 6}

(iii)

Find the range of RR.

Answer

Range of R = {1, 2, 3, 4, 6}

Explanation

To write the relation in roster form, we check every element 'a' in set A against every element 'b' in set A to see if 'b' is exactly divisible by 'a'. The domain is the set of all first elements of the ordered pairs in R, and the range is the set of all second elements. Since every element in A is divisible by itself and by 1, and all resulting values lie within A, the domain and range are identical to set A.

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