The sets A, B, and C are as follows:
A is the set of multiples of 2 = {2, 4, ...}
B is the set of multiples of 3 = {3, 6, ...}
C is the set of multiples of 4 = {4, 8, ...}
(a) Write down a number that is in A ∩ B ∩ C - Junior Cycle Mathematics - Question 5 - 2019
Question 5
The sets A, B, and C are as follows:
A is the set of multiples of 2 = {2, 4, ...}
B is the set of multiples of 3 = {3, 6, ...}
C is the set of multiples of 4 = {4, ... show full transcript
Worked Solution & Example Answer:The sets A, B, and C are as follows:
A is the set of multiples of 2 = {2, 4, ...}
B is the set of multiples of 3 = {3, 6, ...}
C is the set of multiples of 4 = {4, 8, ...}
(a) Write down a number that is in A ∩ B ∩ C - Junior Cycle Mathematics - Question 5 - 2019
Step 1
(a) Write down a number that is in A ∩ B ∩ C.
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Answer
A number that is in A ∩ B ∩ C is 12, as it is a multiple of 2, 3, and 4.
Step 2
(b) Explain why C is a subset of A.
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Answer
Set C consists of multiples of 4, which are all even numbers (e.g., 4, 8, 12). Since all multiples of 4 can be expressed as multiples of 2, it follows that C is entirely contained within A.
Step 3
(c) Because C is a subset of A, there are two regions in the Venn diagram that have no elements. Write an X in each of these regions in the Venn diagram above.
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Answer
In the Venn diagram, the two regions that have no elements are labeled as X in the appropriate areas.
Step 4
(d) Each of the other five regions in the Venn diagram has some elements. In each of these five regions in the Venn diagram above, write one of the elements in that region.
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Answer
Each of the regions can contain elements such as:
In the region exclusive to A: 2
In the region exclusive to B: 3
In the region exclusive to C: 4
In the intersection of A and B (not C): 6
In the intersection of A and C (not B): 8
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