Question

If A= {1,2,3,4), B ={5, 6,7,8} and C= {8,9,10), then AUCUC is

a) {1,2,3,4,5,6,7,8,9,10}
b) {1,2,3,4,5,6,7,9,10}
c) {1,2,3,4,5,6,7}
d) {1,2,3,4,8,9,10}

Answer 1

The union of sets A= {1,2,3,4}, B= {5, 6,7,8}, and C= {8,9,10} is {1,2,3,4,5,6,7,8,9,10}. The operation includes combining all elements without repetitions, therefore option (a) is the correct answer.

Step-by-step explanation:

The student is asked to find the union of sets A, B, and C. To clarify, the union of sets is the set containing all the elements from the given sets, without any duplicates. Given the sets are A= {1,2,3,4}, B= {5, 6,7,8} and C= {8,9,10}, we combine their elements to get A union B union C, which includes every distinct element from all three sets.

Firstly, list out all the elements from set A: {1,2,3,4}.
Next, add the elements from set B that are not already in set A: {5, 6,7,8}.
Finally, add the elements from set C that are not already in the union of sets A and B: {8,9,10}. Note that 8 is already included from set B, so it is not added again.

The final union set is AUCUC = {1,2,3,4,5,6,7,8,9,10}, which corresponds to option (a).