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Mathematics Question on Differential Calculus

Let Ω=1,2,3,4,5,6\Omega = \\{1,2,3,4,5,6\\}. Then which of the following classes of sets is an algebra?

A

F1=∅,Ω,1,2,3,4,3,6\mathcal{F}_1 = \\{\emptyset, \Omega, \\{1,2\\}, \\{3,4\\}, \\{3,6\\}\\}

B

F2=∅,Ω,1,2,3,4,5,6\mathcal{F}_2 = \\{\emptyset, \Omega, \\{1,2,3\\}, \\{4,5,6\\}\\}

C

F3=∅,Ω,1,2,4,5,1,2,4,5,3,4,5,6,1,2,3,6\mathcal{F}_3 = \\{\emptyset, \Omega, \\{1,2\\}, \\{4,5\\}, \\{1,2,4,5\\}, \\{3,4,5,6\\}, \\{1,2,3,6\\}\\}

D

F4=∅,4,5,1,2,3,6\mathcal{F}_4 = \\{\emptyset, \\{4,5\\}, \\{1,2,3,6\\}\\}

Answer

F2=∅,Ω,1,2,3,4,5,6\mathcal{F}_2 = \\{\emptyset, \Omega, \\{1,2,3\\}, \\{4,5,6\\}\\}

Explanation

Solution

The correct option is (B): F2=∅,Ω,1,2,3,4,5,6\mathcal{F}_2 = \\{\emptyset, \Omega, \\{1,2,3\\}, \\{4,5,6\\}\\}