The universal set, U , is U = { A , B , C , . . . . , Z } .

Question

. The universal set, U , is U = { A , B , C , . . . . , Z } . The set W is the letters in the word “TROMBONE“ . The set X is the letters in the word “SAXAPHONE”. And the set Y is the letters in the word “CLARINET”. What is the cardinality of the set ( W È X )’ Ç Y ?

Answer 1

We need to find:

(W∪X)′∩Y Step 1: Write the sets

W = letters in “TROMBONE”

Ignoring repeated letters:

W={T,R,O,M,B,N,E} X = letters in “SAXAPHONE”

X={S, A, X, P, H, O, N, E} Y = letters in “CLARINET”

Y={C, L, A, R, I, N, E, T} Step 2: Find W∪X

W∪X={T,R,O,M,B,N,E,S,A,X,P,H} Step 3: Find (W∪X)′

The universal set contains A–Z. We need the letters not in W∪X.

(W∪X)′={C,D,F,G,I,J,K,L,Q,U,V,W,Y,Z}Step 4: Intersect with Y

Y={C,L,A,R,I,N,E,T}Common letters are:

(W∪X)′∩Y={C,L,I}Therefore,

the cardinality is:

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