Question

1. Let D=​{1212​,1515​,1717​}, E=​{1212​,1414​,1515​,1616​} and F=​{1111​,1313​,1414​,1515​,1717​}.

List the elements in the set​ (D∪​E)∩F.

​(D∪​E)∩F=

2. Let U = { 1,7,9,11,13,16,17,18,19}, X = {7,11,16,18}, Y = {7,9,11,13,16}, and Z = { 1,7,9,18,19}. List the members of the given set, using set braces.

(X∩Y′)∪(Z′∩Y′)

(X∩Y′)∪(Z′∩Y′)=

3. Use the union rule to answer the question.

If n(B) = 16, n(A ∩ B)=5 , and (A ∪ B) =17​,

n(A)?

Answer 1

Hey,

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1)

Given D=​{1212​,1515​,1717​}, E=​{1212​,1414​,1515​,1616​} and F=​{1111​,1313​,1414​,1515​,1717​}.

So, DUE={1212​,1515​,1717​,1414,1616}

So, (DUE)∩F={1414​,1515​,1717​}

2)

Given U = { 1,7,9,11,13,16,17,18,19}, X = {7,11,16,18}, Y = {7,9,11,13,16}, and Z = { 1,7,9,18,19}

(X∩Y′)={18}

Z'={11,13,16,17}

Y'={1,17,18,19}

(Z′∩Y′)={17}

So,

(X∩Y′)U(Z′∩Y′)={17,18}

3)

n(AUB)=n(A)+n(B)-n(A∩B)

So, n(A)=17-16+5=6

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Thanks.