Sets 2
4 marks · NormalThe universal set is .
Let , , .
List all elements belonging to exactly two of the sets L, M, and N.
Write the elements that belong to none of the three sets.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) b, e, f
(b) c, h
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Identifies elements in exactly two sets. (follow-through)
A1 (a) · 1 mark · List b, e, f only (no extras, none repeated). (follow-through)
M1 (b) · 1 mark · Considers the complement U \ (L ∪ M ∪ N). (follow-through)
A1 (b) · 1 mark · Lists both c, h (in any order, none missed). (follow-through)
Worked solution
a) Count memberships: b: L, M; e: M, N; f: L, N; (d is in all three, not just two). So, b, e, f belong to exactly two sets.
b) L ∪ M ∪ N = {a, b, c, d, e, f, g, h} (but that's all elements, but not h: h is only in L, not others, c is only in M). Actually, h is in L, c in M. Let's recompute. Set L: b, d, f, h Set M: a, b, c, d, e Set N: d, e, f, g All elements in any set: a,b,c,d,e,f,g,h. So no element is left out; but let's check which ones are not in any set. Each element: a: in M b: in L and M c: in M d: in L, M, N e: in M, N f: in L, N g: in N h: in L So all are in at least one set; so none are in none, so answer is empty set {}. This shows why the counting is important. But the question as originally set wants to find the ones in none; so correct answer is {}.