Fsc Part 1 Mathematics (Complete Solution)

Q7
If U={1,2,3,.....,20} and A={1,3,5,...........,19}, verify the following

(i) AUAc=U

SOLUTION:

L.H.S=AUAc

=AU(U-A)

={1,3,5,........,19}U({1,2,3,.......,20}-{1,3,5,......19})

={1,3,5,.....,19}U{2,4,6,........,20}

={1,2,3,4,.............,20}

=U

Hence  AUAc=U

(ii) A∩U=A

SOLUTION:

L.H.S=A∩U

={1,3,5,.......,19}∩{1,2,3,.........20}

={1,3,5,.........19}

=A

=R.H.S

Hence A∩U=A

(iii) A∩Ac= Φ

SOLUTION:

L.H.S=A∩Ac

=A∩(U-A)

={1,3,5,..........,19}∩({1,2,3,4,5,.............,20}-{1,3,5,...........,19})

={1,3,5,.............,19}∩{2,4,6,..........,20}

={   }

=R.H.S

Hence  A∩Ac= Φ

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