12. In study of a certain university, the following data were collected. There were 30 students
taking mathematics, 28 students taking physics and 43 taking English. 14 students were
taking mathematics and physics, 15 students were taking mathematics and English and 19
students were taking physics and English, 6 students were taking all the three subjects.
a. How many students were taking physics only?
b. How many students were taking mathematics and English but not physics?
c. How many students were taking exactly one of these subjects?
d. Draw a Venn diagram.
13. Find an odd natural number x such that LCM(x,40) = 1400.
14. Two incandescent lamps are turned on at the same time. One blinks every 4 seconds and
the other blinks every 6 seconds. In 60 seconds, how many times will they blink at the
same time?​