Question 6 of 33intermediate🔍 AnalyzeShort Answer3 marks

Let A={1,2,3,4}A = \{1, 2, 3, 4\}, B={1,5,9,11,15,16}B = \{1, 5, 9, 11, 15, 16\} and f={(1,5),(2,9),(3,1),(4,5),(2,11)}f = \{(1,5), (2,9), (3,1), (4,5), (2,11)\} Are the following true?

(i)

ff is a relation from AA to BB

Answer

True. f is a relation from A to B.

(ii)

ff is a function from AA to BB. Justify your answer in each case.

Answer

False. f is not a function from A to B.

Explanation

For part (i), a relation from A to B is a subset of A × B. Checking each ordered pair in f: (1,5), (2,9), (3,1), (4,5), (2,11) — all first elements belong to A and all second elements belong to B. Hence f ⊆ A × B, making it a relation. For part (ii), a function requires that each element of A has exactly one image in B. Here, element 2 ∈ A has two images: 9 and 11 (from pairs (2,9) and (2,11)). This violates the definition of a function, so f is not a function from A to B.

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