Sir/ Madam
 
Can you please by using equations step by step derive the formula n left parenthesis A union B union C right parenthesis equals space n left parenthesis A right parenthesis plus n left parenthesis B right parenthesis plus n left parenthesis C right parenthesis minus n left parenthesis A intersection B right parenthesis minus n left parenthesis B intersection C right parenthesis minus n left parenthesis A intersection C right parenthesis plus n left parenthesis A intersection B intersection C right parenthesis use venn diagrams too if possible?

Asked by Varsneya Srinivas | 18th May, 2016, 10:56: AM

Expert Answer:

Formulas space used
straight n open parentheses straight X union straight Y close parentheses space equals space straight n open parentheses straight X close parentheses plus straight n open parentheses straight Y close parentheses minus straight n open parentheses straight X intersection straight Y close parentheses
space straight n open square brackets open parentheses straight X union straight Y close parentheses intersection straight Z close square brackets space equals space straight n open square brackets open parentheses straight X intersection straight Z close parentheses union open parentheses straight Y intersection straight Z close parentheses close square brackets
space straight n open square brackets open parentheses straight X intersection straight Z close parentheses intersection open parentheses straight Y intersection straight Z close parentheses close square brackets space equals space straight n open parentheses straight X intersection straight Y intersection straight Z close parentheses



straight n open parentheses straight A union straight B union straight C close parentheses space equals space straight n open square brackets open parentheses straight A union straight B close parentheses union straight C close square brackets
equals straight n open parentheses straight A union straight B close parentheses space plus space straight n open parentheses straight C close parentheses space minus space space straight n open square brackets open parentheses straight A union straight B close parentheses intersection straight C close square brackets
equals straight n open parentheses straight A close parentheses plus straight n open parentheses straight B close parentheses space minus space straight n open parentheses straight A intersection straight B close parentheses space plus space straight n open parentheses straight C close parentheses space minus space space straight n open square brackets open parentheses straight A union straight B close parentheses intersection straight C close square brackets space
equals straight n open parentheses straight A close parentheses plus straight n open parentheses straight B close parentheses space minus space straight n open parentheses straight A intersection straight B close parentheses space plus space straight n open parentheses straight C close parentheses space minus space space straight n open square brackets open parentheses straight A intersection straight C close parentheses union open parentheses straight B intersection straight C close parentheses close square brackets space
equals straight n open parentheses straight A close parentheses plus straight n open parentheses straight B close parentheses space minus space straight n open parentheses straight A intersection straight B close parentheses space plus space straight n open parentheses straight C close parentheses space minus space space straight n open parentheses straight A intersection straight C close parentheses space minus straight n open parentheses straight B intersection straight C close parentheses plus straight n open square brackets open parentheses straight A intersection straight C close parentheses intersection open parentheses straight B intersection straight C close parentheses close square brackets
equals straight n open parentheses straight A close parentheses plus straight n open parentheses straight B close parentheses space minus space straight n open parentheses straight A intersection straight B close parentheses space plus space straight n open parentheses straight C close parentheses space minus space space straight n open parentheses straight A intersection straight C close parentheses space minus straight n open parentheses straight B intersection straight C close parentheses plus straight n open parentheses straight A intersection straight B intersection straight C close parentheses
equals straight n open parentheses straight A close parentheses plus straight n open parentheses straight B close parentheses space plus space space straight n open parentheses straight C close parentheses minus space straight n open parentheses straight A intersection straight B close parentheses space minus space space straight n open parentheses straight A intersection straight C close parentheses space minus straight n open parentheses straight B intersection straight C close parentheses plus straight n open parentheses straight A intersection straight B intersection straight C close parentheses

Answered by Vijaykumar Wani | 18th May, 2016, 11:12: AM