Fsc Part 1 Mathematics (Complete Solution)

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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) A ^{c}**

SOLUTION:

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

= {1,3,5,7,9}

**(ii) B ^{c}**

SOLUTION:

B^{c} = 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) A ^{c} U C^{c}**

SOLUTION:

A^{c}UC^{c}= {1,3,5,7,9} U {2,4,6,8,10}

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

**(vii) A ^{c }∩ C**

SOLUTION:

A^{c} ∩ C= {1,3,5,7,9} U {1,3,5,7,9}

= {1,3,5,7,9}

**(viii) U ^{c}**

SOLUTION:

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