cofinite topology,standard topology,half-open interval topology

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1.$R$ be equipped with the cofinite topology. Is $R$ connected?

2.$R$ be equipped with the standard topology. Is $R$ connected?

3.$R$ be equipped with the half-open interval topology. Is $R$ connected?

I think that 3 is FALSE. but I don't know that 1,2 are connected

How should i prove that first and second are connected?

Thank you for your answer.