Question 143080
I'll do the first four to get you started



a)


*[Tex \LARGE A \bigcup B] is simply the union between the two sets. So simply take all of the uniqe elements of each set and put them together in the new set *[Tex \LARGE A \bigcup B]


So

 *[Tex \LARGE A \bigcup B=\left\{b,c,d,e,f,g\right\}]



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b)




*[Tex \LARGE A \bigcap B] is simply the intersection between the two sets. So whatever elements in two sets have in common will make up *[Tex \LARGE A \bigcap B] (which in English says "set A intersect with set B")



Since set A and set B have the element "c" in common, this means the intersection of sets A and B gives us:


*[Tex \LARGE A \bigcap B=\left\{c\right\}]



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c)


The notation A' simply means the set of every letter that is NOT in set A. So A' is the entire alphabet but with the letters b,c, and d taken out of it


So


*[Tex \LARGE A^\prime=\left\{a,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z\right\}]





The notation B' simply means the set of every letter that is NOT in set B. So B' is the entire alphabet but with the letters c, e, f, and g taken out of it


So


*[Tex \LARGE B^\prime=\left\{a,b,d,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z\right\}]



Now let's take the intersection between the two sets.



Since set A' and set B' have the elements a, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, and z in common, this means the intersection of sets A' and B' gives us:


*[Tex \LARGE A^\prime  \bigcap B^\prime =\left\{a,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z\right\}]




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d)



Using the same sets A' and B' from part c)





*[Tex \LARGE A^\prime \bigcup B^\prime] is simply the union between the two sets. So simply take all of the uniqe elements of each set and put them together in the new set *[Tex \LARGE A^\prime \bigcup B^\prime]


So

 *[Tex \LARGE A^\prime \bigcup B^\prime=\left\{a,b,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z\right\}]