# There was a question in my exam discrete maths that I just couldn't figure out. I know it's supposed to be solved using the inclusion-exclusion principle. anyone able to help me solve and understand this question. For a survey, 200 people are asked about which forms of transport the had used in the last month it was found that 150 used trains, 80 had cycled and used trains, and 180 had used one or the other of these two forms of transport. Question: How many people had cycled in the last month? Question: How many had not used either form of transport.

There was a question in my exam discrete maths that I just couldn't figure out. I know it's supposed to be solved using the inclusion-exclusion principle. anyone able to help me solve and understand this question.
For a survey, 200 people are asked about which forms of transport the had used in the last month it was found that
150 used trains,
80 had cycled and used trains, and
180 had used one or the other of these two forms of transport.
Question: How many people had cycled in the last month?
Question: How many had not used either form of transport.
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lefeuilleton42
LET c and t denote cycle and train.
$c\cup t=180$
$c\cap t+80$
t=150
180=c+150−80
c=110
Those who did not use any of the two transportations are
200−180=20