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- In a freshman class of 68 high school students, 20 students are taking history, 40 students are takingmath, and 15 students are taking both history and math. Draw a Venn diagram to represent thissituation. Label each part of the diagram clearly.In Exereises 6 and 7, let p, q, and r be the following state- ments: p: I will study discrete structure; q: I will go to a movie; r: I am in a good mood. 6. Write the following statements in terms of p, q, r, and logical connectives. (a) If1 am not in a good mood, then I will go to a movie. (b) I will not go to a movie and I will study discrete structures, (c) I will go to a movie only if I will not study discrete structures. (d) IfI will not study discrete structures, then I am not in a good mood.Construct a Venn diagram to answer the question. Doctor X and Doctor Y have 24 patients. 12 patients have fever, 6 patients have colds, 15 patients have headache. 1 patient has all three sicknesses. 2 patients have fever and colds, but no headache. 2 patients have colds and headache, but no fever. If all the patients of Doctor X and Doctor Y have at least one of the mentioned sickness, how many patients have fever and headache, but no colds?
- Suppose that |A| = m and |B| = n. Find the following cardinalities.Draw a Venn diagram so that N(U) = 15, n(S) = 10, n(T)= 4, n(SUT) = 13In a certain school, 50 students in a certain class were enrolled in three subjects as follows:30 enrolled in Algebra20 enrolled in Physics25 enrolled in Chemistry14 enrolled in Chemistry and Algebra12 enrolled in Chemistry and Physics11 enrolled in Algebra and Physics5 enrolled in all three subjects Use the venn diagram to solve the following question, how many students were enrolled ina.) exactly one subjectb.) Algebra and Physics but not Chemistryc.) Did not enroll in any of the threed.) At most two subjects
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