Discrete math sets help?How would I do this question?Suppose U = { 1 , 2......

valtricotinevh

valtricotinevh

Answered

2022-07-15

Discrete math sets help?
How would I do this question?
Suppose U = { 1 , 2... , 9 }, A = all multiples of 2, B = all multiples of 3, and C = { 3 , 4 , 5 , 6 , 7 }. Find C ( B A ).

Answer & Explanation

Rihanna Robles

Rihanna Robles

Expert

2022-07-16Added 18 answers

Step 1
The multiples of 3 in U are 3,6, and 9, so B = { 3 , 6 , 9 }. The multiples of 2 in U are 2,4,6, and 8, so A = { 2 , 4 , 6 , 8 }. For any sets X and Y, the set difference X∖Y is the set of objects that are in X but not Y. Thus, B∖A is the set of digits that are in B but not in A. Look at the members of B: 3 and 9 are in B but not A, so they’re in B∖A. 6, on the other hand, is in B and A, so it’s not in B∖A. And nothing else is in B, never mind whether it’s in A or not, so nothing else is in B∖A. Thus, B A = { 3 , 9 }.
Step 2
Now see if you can apply the same sort of reasoning to find C∖{3,9}.
Lorelei Patterson

Lorelei Patterson

Expert

2022-07-17Added 6 answers

Step 1
If B is the set of multiples of 3 in the universe, then the elements of B are just 3,6,9; that is,
B = { 3 , 6 , 9 }
Step 2
Likewise, A is the set of even numbers inside U, so A = { 2 , 4 , 6 , 8 }. Then B A is the set of things in B that aren't in A. We see that 3 and 9 are in B not in A, so B A = { 3 , 9 }

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