Photo AI
A, B, and C are sets - Junior Cycle Mathematics - Question 7 - 2021
Question 7
A, B, and C are sets. Complete the tables below by shading in each of the given sets in the Venn diagram. Set A ∪ B Venn diagram Set A ∩ (B ∩ C) Venn diagr... show full transcript
Worked Solution & Example Answer:A, B, and C are sets - Junior Cycle Mathematics - Question 7 - 2021
Step 1
Complete the tables below by shading in each of the given sets in the Venn diagram.
Answer
To complete the shading for the Venn diagram:
- For A ∪ B: Shade the entire area that is covered by either set A or set B. This includes the overlap area as well.
- For A ∩ (B ∩ C): Shade only the area that is common to A, B, and C. This is the area where all three sets overlap.
Step 2
(i) Write an X in the region of the Venn diagram below which must contain no elements.
Answer
In the Venn diagram for sets P and Q, place an 'X' in the area that represents the region where P does not have any elements that are also in Q. Specifically, since P is a subset of Q, the area unique to Q that does not overlap with P should contain the 'X'.
Step 3
(ii) Put a tick (✓) in the correct box to show which statement must be true.
Answer
The statement that must be checked is # P ⊆ Q. This must be true because, by definition, a subset means that all elements of P are contained within Q. Therefore, I would place a tick (✓) in the box for # P ⊆ Q and explain that since P is defined to be a subset of Q, it is always true that P is either equal to or contained within Q.