Question 1131781
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}