Consider the 3-circle Venn Diagram, with three sets A, B, and C. Let A, B, and...

 

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Consider the 3-circle Venn Diagram, with three sets A, B, and C. Let A, B, and C be the cardinality of the three sets, respectively. B. C (a) If there are two sets, the Inclusion-Exclusion Principle tells us that |AUB=A+B-AnB. What if there are three sets? Determine the correct formula for AUBUC, and clearly explain why your formula is correct. (b) Let S be the set of positive integers less than 1000 that contains at least one digit equal to 5. For example, all of these numbers are in set S: 5, 35, 50, 55, 558, 750, 905. There are many others. Determine S, the number of elements in set S. Clearly justify your answer. (c) Let T be the set of positive integers less than 1000 that is divisible by at least one of these three numbers: 7, 11, 13. For example, all of these numbers are in set T: 13, 77, 98, 121, 715, 994. There are many others. Determine 7, the number of elements in set T. Clearly justify your answer. Consider the 3-circle Venn Diagram, with three sets A, B, and C. Let A, B, and C be the cardinality of the three sets, respectively. B. C (a) If there are two sets, the Inclusion-Exclusion Principle tells us that |AUB=A+B-AnB. What if there are three sets? Determine the correct formula for AUBUC, and clearly explain why your formula is correct. (b) Let S be the set of positive integers less than 1000 that contains at least one digit equal to 5. For example, all of these numbers are in set S: 5, 35, 50, 55, 558, 750, 905. There are many others. Determine S, the number of elements in set S. Clearly justify your answer. (c) Let T be the set of positive integers less than 1000 that is divisible by at least one of these three numbers: 7, 11, 13. For example, all of these numbers are in set T: 13, 77, 98, 121, 715, 994. There are many others. Determine 7, the number of elements in set T. Clearly justify your answer.