Question

Select the definitions for sets A and B below that show that the set equation given below is not a set identity. (B-A)uA=B

a)A (1) and B = {1}
b)A (1, 2) and B = {2,3]
c)A= (1) and B = {1, 2}
d)A=(2, 4, 5) and B = {1, 2, 3, 4, 5)

Answer 1

To determine if the set equation (B-A)uA=B is a set identity, we must select definitions for sets A and B. Option (b) and (d) show that the set equation is not a set identity.

Step-by-step explanation:

In order to determine if the set equation (B-A)uA=B is a set identity, we need to select definitions for sets A and B that show it is not true. Let's go through the options:

1. A (1) and B = {1}: In this case, (B-A)uA = ({1}-{1})u{1} = {}u{1} = {1}. But B = {1} doesn't equal {1}, so this option is incorrect.
2. A (1, 2) and B = {2,3]: In this case, (B-A)uA = ({2,3}-{1,2})u{1,2} = {3}u{1,2} = {1,2,3}. But B = {2,3] doesn't equal {1,2,3}, so this option is incorrect.
3. A= (1) and B = {1, 2}: In this case, (B-A)uA = ({1,2}-{1})u{1} = {2}u{1} = {1,2}. But B = {1,2} does equal {1,2}, so this option is a valid set identity.
4. A=(2, 4, 5) and B = {1, 2, 3, 4, 5}: In this case, (B-A)uA = ({1,2,3,4,5}-{2,4,5})u{2,4,5} = {1,3}u{2,4,5} = {1,2,3,4,5}. But B = {1,2,3,4,5} does equal {1,2,3,4,5}, so this option is also a valid set identity.

Therefore, options (b) and (d) show that the set equation is not a set identity.