Q. 23.7( 10 Votes )

If A = {1, 2, 3,

Answer :

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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