Answer
(AUB)∩(AUC) = {a,b,g,h}
Work Step by Step
U={a,b,c,d,e,f,g,h}
A={a,g,h}
B={b,g,h}
C={b,c,d,e,f}
To find (AUB)∩(AUC), we need to find (AUB) and (AUC).
AUB={a,g,h}U{b,g,h}={a,b,g,h}
(List of all elements of A and the elements of B that are not in A)
AUC={a,g,h}U{b,c,d,e,f}={a,b,c,d,e,f,g,h}
(List of all elements of A and the elements of C that are not in A)
(AUB)∩(AUC)={a,b,g,h} ∩ {a,b,c,d,e,f,g,h} = {a,b,g,h}
(Common elements of (AUB) and (AUC))
