Put a tick (✔️) in the correct box in each row of the table below to show whether each statement is always true, sometimes true, or never true, for three different sets A, B, and C - Junior Cycle Mathematics - Question 4 - 2016
Question 4
Put a tick (✔️) in the correct box in each row of the table below to show whether each statement is always true, sometimes true, or never true, for three different s... show full transcript
Worked Solution & Example Answer:Put a tick (✔️) in the correct box in each row of the table below to show whether each statement is always true, sometimes true, or never true, for three different sets A, B, and C - Junior Cycle Mathematics - Question 4 - 2016
Step 1
A ∩ B = B ∩ A
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Answer
This statement is always true due to the commutative property of intersection. In set theory, the intersection operation is commutative, meaning that the order of the sets does not affect the result.
Step 2
A ∪ B = B ∪ C
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Answer
This statement is sometimes true. It can be true in specific cases where the union of sets A and B results in the same elements as the union of sets B and C, but this is not universally applicable.
Step 3
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
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Answer
This statement is always true. This is known as the distributive law of sets, which states that the intersection distributes over union.
Step 4
A ∪ C = A ∩ C
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Answer
This statement is never true. The union of two sets A and C contains all elements from both sets, whereas the intersection only contains shared elements. Generally, A ∪ C is not equal to A ∩ C.
Step 5
A ∩ B = { }
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Answer
This statement is sometimes true. It is true if sets A and B are disjoint (i.e., they have no elements in common). However, it can also be false if A and B share elements.
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