Question 1131781: Can someone please explain this to me? I am completely lost!
Thanks.
U = {a,b,c,d,e,f,g,h,i,j,}
A = {a, c, e, g, i}
B = {b, d, f, h, j}
C = {a, b, d}
1. Determine 𝐴′ ∩ 𝐵
2. Determine (𝐴 ∪ 𝐶) − (𝐴 ∩ 𝐶)
3. Determine Determine 𝐵′ ∩ 𝐶′
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! U = {a,b,c,d,e,f,g,h,i,j,}
A = {a, c, e, g, i}
B = {b, d, f, h, j}
C = {a, b, d}
1. Determine 𝐴′ ∩ 𝐵
2. Determine (𝐴 ∪ 𝐶) − (𝐴 ∩ 𝐶)
3. Determine Determine 𝐵′ ∩ 𝐶′
The complement of a set A, denoted by 𝐴′ , is the set of all elements that are in the universal set U but are not in A.
𝐴′ ∩ 𝐵 ={b,d,f,h,j}
B = {b, d, f, h, j}
intersection 𝐴′ ∩ 𝐵 is defined as the set consisting of the elements that are common in 𝐴′and B
=>𝐴′ ∩ 𝐵 ={b,d,f,h,j}
2. Determine (𝐴 ∪ 𝐶) − (𝐴 ∩ 𝐶)
The union of two sets is a set containing all elements that are in A or in C
if
A = {a, c, e, g, i}
C = {a, b, d}
=> (𝐴 ∪ 𝐶)={a, b,c,d, e, g, i}
=>(𝐴 ∩ 𝐶) ={a}
(𝐴 ∪ 𝐶) − (𝐴 ∩ 𝐶) ={a, b,c,d, e, g, i}-{a}={b,c,d, e, g, i}
3. Determine Determine 𝐵′ ∩ 𝐶′
𝐵′ the new set gets everything that is in the universe but is outside of B
𝐶′ the new set gets everything that is in the universe but is outside of C
U = {a,b,c,d,e,f,g,h,i,j}
B = {b, d, f, h, j}
𝐵′ ={a,c,e,g,i}
U = {a,b,c,d,e,f,g,h,i,j}
C = {a, b, d}
𝐶′ ={c,e,f,g,h,i,j}
𝐵′ ∩ 𝐶′={a,c,e,g,i} ∩ {c,e,f,g,h,i,j}={e,g,i}
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