Question - Set Theory and Relations Worksheet
Solution:
This image appears to show a question from an academic worksheet or test, related to set theory and relations.(a) The first part of the question asks you to state the (i) object part 3, (ii) the relation in the form of a set of ordered pairs.From the diagram, we can see that Set A includes the elements {1, 2, 3, 4} and Set B includes the elements {5, 6, 7, 8}.(i) The object part 3 in Set A appears to be related to the number 7 in Set B.(ii) As for the relation in the form of a set of ordered pairs, we would read the arrows connecting elements of Set A to elements of Set B to form these pairs. The complete set of ordered pairs, assuming we can see all links between the sets, appears to be:R = {(1, 5), (1, 6), (2, 6), (2, 7), (3, 7), (4, 8)}(b) For the second part of the question, we need to determine whether this relation is a function or not and provide reasoning for the answer.A relation from Set A to Set B is a function if and only if every element of Set A is related to no more than one element in Set B. Looking at the ordered pairs and the diagram:1 is related to 5 and 6, which is more than one element of Set B.2 is related to 6 and 7, which is more than one element of Set B.3 is related only to 7.4 is related only to 8.Since at least one element of Set A (specifically 1 and 2) is related to more than one element of Set B, the relation is NOT a function.Thus, your answer to part (b) would be that the relation is not a function because there exists an element in Set A that is related to more than one element in Set B.
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