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In each of (a)−(f), answer the following questions: Is A⊆B ? Is B⊆A ? Is either A or B a proper subset of the other? (a) A={6,{6},( 6) 2 },B={6,{6},{{6}}} Is A⊆B ? Yes No Is B⊆A ? Yes No Is either A or B a proper subset of the other? Yes, A is a proper subset of B. Yes, B is a proper subset of A. No, neither is a proper subset of the other. (b) A={3, 5 2 −4 2 ,24mod7},B={8mod5} is A⊂B ? Y Yes No Is B∈A ? Y res Is either A or B a proper subset of the other? Yes, A is a proper subset of B. Yes, 8 is a proper subset of A. No, neither is a proper subset of the othen (c) A=((1,2},{2,3),B=(1,2,3) is A⊆B ? (d) A={a,b,c},B={{a},{b},{c}} Is A⊆B ? Yes No Is B⊆A ? Yes No Is either A or B a proper subset of the other? Yes, A is a proper subset of B. Yes, B is a proper subset of A. No, neither is a proper subset of the other. (e) A={9
,{3}},B={3} Is A CB? Yes No Is B⊂A ? Yes No Is either A or B a proper subset of the other? Yes, A is a proper subset of B. Yes, B is a proper subset of A. No, neither is a proper subset of the other. (f) A={x∈R∣cos(x)∈Z},B=(x∈R∣sin(x)∈Z} is A⊂B7 Yes No ts B⊂A क ? yes No Is eitheri A or e a proper subset of the other? Yes, A is a proper subget of B. Yno, B is a proper subset of A

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