I need help with this problem with all three parts of it. I have to use the diagram that I am attaching to help me answer these questions. a) Does the order of operations matter for the expression A ∪ B ∩ C? Why or why not? (Other ways to ask this question: Is A ∪ B ∩ C ambiguous without the parentheses? Do we need to indicate whether the union or intersection should be performed first, or does it not matter? Why or why not?) b) How are A ∪ (B ∩ C) and (A ∪ B) ∩ C related as sets? (Are they always equal? If so, how do you know? If not, is one always a subset of the other? If so, which one is a subset of the other? If not, how do you know?) c) Under what circumstances would A ∪ (B ∩ C) = (A ∪ B) ∩ C? How would A, B, and C have to be related in this case? List all the way this could happen.
I need help with this problem with all three parts of it. I have to use the diagram that I am attaching to help me answer these questions.
a) Does the order of operations matter for the expression A ∪ B ∩ C? Why or why not? (Other ways to ask this question: Is A ∪ B ∩ C ambiguous without the parentheses? Do we need to indicate whether the union or intersection should be performed first, or does it not matter? Why or why not?)
b) How are A ∪ (B ∩ C) and (A ∪ B) ∩ C related as sets? (Are they always equal? If so, how do you know? If not, is one always a subset of the other? If so, which one is a subset of the other? If not, how do you know?)
c) Under what circumstances would A ∪ (B ∩ C) = (A ∪ B) ∩ C? How would A, B, and C have to be related in this case? List all the way this could happen.
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