Out of 14 people, twelve said that it was not the case that they watched television but did not listen to the radio. Also, for nine people it is not the case that they do not watch TV and do not listen to the radio. Finally, seven people either watch television or listen to the radio but do not do both. Noe let A be number of people that watch TV and B be the number of people that listen radio. Find A and B.

Asked by Anil | 20th May, 2017, 04:24: PM

Expert Answer:

begin mathsize 16px style space twelve space said space that space it space was space not space the space case space that space they space watched space television space but space did space not space listen space to space the space radio.
rightwards double arrow straight n left parenthesis straight A intersection straight B apostrophe right parenthesis apostrophe equals 12
rightwards double arrow straight n left parenthesis straight A apostrophe union straight B right parenthesis equals 12
for space nine space people space it space is space not space the space case space that space they space do space not space watch space TV space and space do space not space listen space to space the space radio
rightwards double arrow straight n left parenthesis straight A apostrophe intersection straight B apostrophe right parenthesis apostrophe equals 9
rightwards double arrow straight n left parenthesis straight A union straight B right parenthesis equals 9................................ left parenthesis straight i right parenthesis
seven space people space either space watch space television space or space listen space to space the space radio space but space do space not space do space bth
rightwards double arrow straight n left parenthesis straight A union straight B right parenthesis minus straight n left parenthesis straight A intersection straight B right parenthesis equals 7
rightwards double arrow 9 minus straight n left parenthesis straight A intersection straight B right parenthesis equals 7 space space space space.................... from space left parenthesis straight i right parenthesis space
rightwards double arrow straight n left parenthesis straight A intersection straight B right parenthesis equals 2 space space space space space space space space space space end style

Answered by Sneha shidid | 21st May, 2017, 11:21: AM