# If A = {1, 2, 3,

Note: In general X Y = {a: a ϵ X or a ϵ Y}

X Y = {a:a ϵ X and a ϵ Y}.

i. A B = {x: x ϵ A or x ϵ B}

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

ii. A C = {x: x ϵ A or x ϵ C}

= {1, 2, 3, 4, 5, 7, 8, 9, 10, 11}

iii. B C = {x: x ϵ B or x ϵ C}

= {4, 5, 6, 7, 8, 9, 10, 11}

iv. B D = {x: x ϵ B or x ϵ D}

= {4, 5, 6, 7, 8, 10, 11, 12, 13, 14}

v. A B = {x: x ϵ A or x ϵ B}

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

A B C = {x: x ϵ A B or x ϵ C}

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

vi. A B = {x: x ϵ A or x ϵ B}

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

A B D = {x: x ϵ A B or x ϵ D}

= {1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14}

vii. B C = {x: x ϵ B or x ϵ C}

= {4, 5, 6, 7, 8, 9, 10, 11}

B C D = {x: x ϵ B C or x ϵ D}

= {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

viii. B C = {x: x ϵ B or x ϵ C}

= {4, 5, 6, 7, 8, 9, 10, 11}

A B C = {x:x ϵ A and x ϵ B C}.

= {4, 5}

ix. (A B) = {x:x ϵ A and x ϵ B}.

= {4, 5}

(B C) = {x:x ϵ B and x ϵ C}

= {7, 8}

(A B) (B C) = {x:x ϵ (A B) and x ϵ (B C)}.

= ϕ

x. A D = {x: x ϵ A or x ϵ D}

= {1, 2, 3, 4, 5, 10, 11, 12, 13, 14}.

B C = {x: x ϵ B or x ϵ C}

= {4, 5, 6, 7, 8, 9, 10, 11}

(A D) (B C) = {x:x ϵ (A D) and x ϵ (B C)}.

= {4, 5, 10, 11}.

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