We are given that,
A=x∈N:3≤x≤13,B=x∈N:x is even,and C=x∈N:x is odd.
then,
A={3,4,5,6,7,8,9,10,11,12,13}B={2,4,6,8,...}C={1,3,5,7,9,......}
a)
A∩B consist of the elements common to both set A and set B.
Therefore,
A∩B={4,6,8,10,12}
b)
A∪B consist of all elements in set A and set B.
Therefore,
A∪B={2,3,4,5,6,7,8,9,10,11,12,13,14,16,18,20,.....}
For this case, A∪B consist of all even numbers and the odd numbers, 3,5,7,9,11,13 in set A.
c)
B∩C consist of elements common to both set B and set C. Clearly, B∩C={∅}. This is because, no element is common to both sets as set B consist of all even numbers and set C consist of all odd numbers. A number can either be even or odd.
d)
B∪C consist of all elements in set B and set C.
Therefore,
B∪C={1,2,3,4,5,6,7,8,9,10,11,12,13,...}. We can observe that this is the set of natural numbers(N) .
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