200 students took part in a survey. To the question "Are you taking History?", 80 replied yes. To the question "Are you taking Math?", 90 replied yes. To the question "Are you taking Math and History?", 20 replied yes. How many students are taking neither Math nor Historv? (Enter vour answer as a single integer)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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200 students took part in a survey. To the question "Are you taking History?", 80 replied yes. To the question "Are you taking Math?", 90 replied yes. To the question "Are you taking Math and History?", 20 replied yes. How many students are taking neither Math nor Historv? (Enter vour answer as a single integer)
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Step 1

We can use the principle of inclusion-exclusion to find the number of students who are not taking either Math or History.

Let M be the set of students taking Math, and H be the set of students taking History. Then we want to find the size of the set M ∪ H^c, where H^c is the complement of H (i.e., the set of students not taking History).

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