Given U ={7,8,9,10,11,12,13,14,15,16}
A={7,9,11,13,15}
B={8,10,12,14,16}
C={7,8,10,11,14,15}
Now complement of se A i.e A^{c} = {8,10,12,14} (Since A^{c} = {x ∈ U : x ∉ A} )
Similarly, B^{c} ={7,9,11,13,15}
and C^{c} = {9,12,13,16}
(a) A^{c} ∩ (B∩C^{c}) = {8,10,12,14} ∩ {12,16} = {12}
(b) (A U B^{c}) U (B∩C^{c}) ={7,9,11,13,15} U {12,16} = {7,9,11,12,13,15,16}
(c) (A U B)^{c} ∩ C^{c} = {Empty} ∩ {9,12,13,16} = {Empty}
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