Question 454159: Can someone help me with the question below, I am lost. Thank you.
Given A = {2, 4, 6}, B = {1, 3, 5}, and C = { 1, 2, 3, 4, 5, 6, 7}. Evaluate each set
a) A ∩ B
b) A U C
c) B U C
d) (A U B) ∩ C
e) A U (B U C)
f) (A ∩ B) ∩ C
g) (A ∩ B) U C
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! Given A = {2,4,6}, B = {1,3,5,6}, and C = {6, 7}. Evaluate each set
Given A = {2,4, 6}, B = {1,3,5,6}, and C = {6, 7}. Evaluate each set
Rule for ᑎ:
1. Substitute the sets for the corresponding symbols
on each side of the ᑎ.
2. Pick ONLY the elements in common to both sets.
3. Put them between braces.
Rule for ᑌ:
1. 1. Substitute the sets for the corresponding symbols
on each side of the ᑌ
2. Pick ALL the elements in either set whether common to both sets
or not.
3. Put those elements between braces.
a) A ᑎ B
1. Substitute the sets for the corresponding symbols
on each side of the ᑎ.
{2,4,6} ᑎ {1,3,5,6}
2. Pick ONLY the elements in common to both sets.
There is only one element in common to both and that is 6
3. Put it between braces:
{6}
That's the answer to a)
------------------------------
b) A ᑌ C
1. Substitute the sets for the corresponding symbols
on each side of the ᑌ.
{2,4,6} ᑌ {6, 7}
2. Pick ALL the elements in either set whether common to both sets
or not. So we pick them all 2, 4, 6, 7. (There is no need to
put 6 twice)
3. Put them between braces:
{2,4,6,7}
That's the answer to b)
------------------------------
c) B ᑌ C
1. Substitute the sets for the corresponding symbols
on each side of the ᑌ.
{1,3,5,6} ᑌ {6, 7}
2. Pick ALL the elements in either set whether common to both sets
or not. So we pick them all 1, 3, 5, 6, 7. (Again there is no need to
put 6 twice)
3. Put them between braces:
{1,3,5,6,7}
That's the answer to c)
------------------------------
d) (A ᑌ B) ᑎ C
({2,4,6) ᑌ {1,3,5,6}) ᑎ {6,7}
Do inside the parentheses first following the rule for ᑌ:
{1,2,3,4,5,6} ᑎ {6,7}
Now follow the rule for ᑎ
{6}
That's the answer to d)
------------------------------
e) A ᑌ (B ᑌ C)
{2,4,6) ᑌ ({1,3,5,6} ᑌ {6,7})
Do inside the parentheses first following the rule for ᑌ:
{2,4,6) ᑌ {1,3,5,6,7}
Now follow the rule for ᑌ
{1,2,3,4,5,6,7}
That's the answer to e)
----------------------------------
f) (A ᑎ B) ᑎ C
({2,4,6) ᑎ {1,3,5,6}) ᑎ {6,7}
Do inside the parentheses first following the rule for ᑎ:
{6} ᑎ {6,7}
Now follow the rule for ᑎ
{6}
That's the answer to f)
------------------------------
g) (A ᑎ B) ᑌ C
({2,4,6) ᑎ {1,3,5,6}) ᑌ {6,7}
Do inside the parentheses first following the rule for ᑎ:
{6} ᑌ {6,7}
Now follow the rule for ᑌ
{6,7}
That's the answer to g)
Edwin
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