Fsc Part 1 Mathematics (Complete Solution)

Q4
Let U={1,2,3,4,5,6,7,8,9,10},A={2,4,6,8,10},B={1,2,3,4,5}and C={1,3,5,7,9} .List the members each of the following sets

(i) Ac

SOLUTION:

Ac = U - A = {1,2,3,4,5,6,7,8,9,10} - {2,4,6,8,10}

              = {1,3,5,7,9} 

(ii) Bc

SOLUTION:

Bc = U - B = {1,2,3,4,5,6,7,8,9,10} - {1,2,3,4,5} = {6,7,8,9,10}

(iii) A U B

SOLUTION:

A U B = {2,4,6,8,10} U {1,2,3,4,5}

        = {1,2,3,4,5,6,8,10} 

(iv) A - B

SOLUTION:

A - B = {2,4,6,8,10} - {1,2,3,4,5}

        = {6,8,10} 

(v) A ∩ C

SOLUTION:

A∩C= {2,4,6,8,10} ∩ {1,3,5,7,9}

      = {   } 

(vi) Ac U Cc

SOLUTION:

AcUCc= {1,3,5,7,9} U {2,4,6,8,10}

         = {1,2,3,4,5,6,7,8,9,10} 

(vii) Ac ∩ C

SOLUTION:

Ac ∩ C= {1,3,5,7,9} U {1,3,5,7,9}

       = {1,3,5,7,9} 

(viii) Uc

SOLUTION:

Uc= U-U = {1,2,3,4,5,6,7,8,9,10} - {1,2,3,4,5,6,7,8,9,10} = {  }

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