The sets A, B, and C are as follows: A = {2, 3, 4, 5, 6}, B = {2, 4, 6, 8, 10}, and C = {1, 4, 8, 12, 14} - Junior Cycle Mathematics - Question a - 2014

The intersection of sets A and B, denoted A ∩ B, is:

A ∩ B = {2, 4, 6}

To find the set difference B ackslash (A ∩ C), we first need A ∩ C. Since A ∩ C = {4}, we then have:

B ackslash (A ∩ C) = {2, 4, 6, 8, 10} ackslash {4} = {2, 6, 8, 10}

First, we find the set differences:

B \ A = {2, 4, 6, 8, 10} \ {2, 3, 4, 5, 6} = {8, 10}

B \ C = {2, 4, 6, 8, 10} \ {1, 4, 8, 12, 14} = {2, 6, 10}

Now we take the union of these two results:

(B \ A) ∪ (B \ C) = {8, 10} ∪ {2, 6, 10} = {2, 6, 8, 10}

A null set can be represented as:

A ∩ C \ B, which has no elements. Therefore, the null set result is denoted as: ∅.