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finding if boolean is ever true by groups in R

I want a simple way to create a new variable determining whether a boolean is ever true in R data frame. Here is and example: Suppose in the dataset I have 2 variables (among other variables which are not relevant) 'a' and 'b' and 'a' determines a group, while 'b' is a boolean with values TRUE (1) or FALSE (0). I want to create a variable 'c', which is also a boolean being 1 for all entries in groups where 'b' is at least once 'TRUE', and 0 for all entries in groups in which 'b' is never TRUE. From entries like below:

a   b
-----
1   1 
2   0
1   0
1   0
1   1
2   0
2   0
3   0
3   1
3   0

I want to get variable 'c' like below:

a   b   c
-----------
1   1   1 
2   0   0
1   0   1
1   0   1
1   1   1
2   0   0
2   0   0
3   0   1
3   1   1
3   0   1
-----------

I know how to do it in Stata, but I haven't done similar things in R yet, and it is difficult to find information on that on the internet. In fact I am doing that only in order to later remove all the observations for which 'c' is 0, so any other suggestions would be fine as well. The application of that relates to multinomial logit estimation, where the alternatives that are never-chosen need to be removed from the dataset before estimation.

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if X is your data frame

library(dplyr)
X <- X %>%
  group_by(a) %>%
  mutate(c = any(b == 1))

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