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MATH 3333Homework Assignment #6Due date: Friday, October 12NAME (Print):1.ALWAYS TRUE, SOMETIMES TRUE, NEVER TRUE.If your answeris “Always True,” justify by quoting a definition or theorem, or by giving a proof.If your answer is “Sometimes True,” give an example where it is true and anexample where it is false. If your answer is ”NEVER TRUE,” justify by quotinga definition or theorem to the contrary, or by giving a proof.(a) If (sn) is a Cauchy sequence, then(sn)is monotone.(b) If(sn)is a convergent sequence and(tn)is bounded, then(sn·tn)isa convergent sequence.1
(c) If(sn)and(tn)are sequences such thatsn> tn>1for alln,and(sn·tn) converges, then both(sn)and(tn) converge.