The Venn diagram below shows the sets A and B - Junior Cycle Mathematics - Question 9 - 2014
Question 9
The Venn diagram below shows the sets A and B.
List the elements of each of the following sets.
(i) A = { }
(ii) A ∩ B = { }
(iii) B \ A = { }
Tom says: "P ∩ Q ... show full transcript
Worked Solution & Example Answer:The Venn diagram below shows the sets A and B - Junior Cycle Mathematics - Question 9 - 2014
Step 1
A = { }
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Answer
The elements in set A, as indicated in the Venn diagram, are:
A={t,a,s,e}
Step 2
A ∩ B = { }
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Answer
The intersection of sets A and B (i.e., common elements) is:
A∩B={a,s}
Step 3
B \ A = { }
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Answer
The elements in set B that are not in set A are:
B∖A={x,m}
Step 4
State whether Tom’s statement is always true, sometimes true, or never true. Justify your answer.
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Answer
Tom’s statement is always true.
Justification:
When elements are present in both sets P and Q, they must necessarily be in set P. Otherwise, since the intersection of P and Q only includes elements that are in P, it will always hold that:
P∩Q⊆P
This means that any element that is part of the intersection must also be an element of P.
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