In a pollution study of 1500 Indian rivers the following data were reported. 520 were polluted by sulphur compunds, 335 were polluted by phosphorous, 425 were polluted by crude oil, 100 were polluted by both crude oil and sulphur compunds, 152 were polluted by sulphate and phosphate compounds only, 150 were polluted by phosphate and crude oil, and 28 were polluted by all 3 compounds. How many of the rivers were polluted by exactly one of the 3 impurities?

Asked by Varshini Srinivasan | 20th Jun, 2014, 07:07: PM

Expert Answer:

U represents the collection of all the Indian rivers.
S represents the rivers polluted by sulphur compunds.
P represents the rivers polluted by phosphorous.
C represents the rivers polluted by crude oil.

n left parenthesis U right parenthesis equals 1500 comma space n left parenthesis S right parenthesis equals space 520 comma space n left parenthesis P right parenthesis equals space 335 comma space n left parenthesis C right parenthesis equals 425 space
Syntax error from line 1 column 445 to line 1 column 460. Unexpected 'compounds'.
The number of rivers polluted by sulpher compound only is given by

n open parentheses S close parentheses minus n left parenthesis C large intersection S right parenthesis minus n left parenthesis S large intersection P right parenthesis plus n left parenthesis S large intersection C large intersection P right parenthesis equals 520 minus 100 minus 152 plus 28 equals 296

The number of rivers polluted by Crude oil only is given by

n open parentheses C close parentheses minus n left parenthesis C large intersection S right parenthesis minus n left parenthesis P large intersection C right parenthesis plus n left parenthesis S large intersection C large intersection P right parenthesis equals 425 minus 100 minus 150 plus 28 equals 203

The number of rivers polluted by phosphate compound only is given by

n open parentheses P close parentheses minus n left parenthesis C large intersection P right parenthesis minus n left parenthesis S large intersection P right parenthesis plus n left parenthesis S large intersection C large intersection P right parenthesis equals 335 minus 150 minus 152 plus 28 equals 61
Total number of rivers polluted by exactly one of the 3 impurities

=296+203+61=560


Answered by Vimala Ramamurthy | 23rd Jun, 2014, 03:35: PM