Problem on set theory and counting


Assignment:

Q1. List the ordered pairs in the equivalence relations produced by these partitions of {0,1,2,3,4,5}
a) {0}, {1,2}, {3,4,5}
b) {0,1}, {2,3}, {4,5}
c) {0,1,2}, {3,4,5}
d) {0}, {1}, {2}, {3}, {4}, {5}

Q2. Which of these collections of subsets are partitions of the set of integers?
a) the set of even integers and the set of odd integers
b) the set of positive integers and the set of negative integers

Q3. Which of these collections of subsets are partitions of {1,2,3,4,5,6}?
a) {1,2}, {2,3,4}, {4,5,6}
b) {1}, {2,3,6}, {4}, {5}
c) {2,4,6}, {1,3,5}
d) {1,4,5}, {2,6}.

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Mathematics: Problem on set theory and counting
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