Are these two definition is contrast to each others?
option (4) says cannot shatter "one of..." says one... but other slides as follows tells us "no set of k+1 points..."
which of them is true for definition of VC ... which part is my wrong point?
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The correct definition is the second one (and the answer (3) from the first part of your question). To quote an authoritative source:
The final ingredient in the Vapnik Chervonenkis theory is an analysis of the case when there is a finite $d$ which is the largest size of shattered set [...] The value $d$ is known as as the Vapnik Chervonenkis (VC) dimension of the class $H$, denoted by VCdim($H$).
(Cristianini and Shawe-Taylor, An Introduction to Support Vector Machines and other kernel-based learning methods, Cambridge University Press 2000, p. 56.)
However, the "definition" you quote in the first part of your question is actually not a definition, but seems to be an exam question. One part of it is about the "most efficient" way of proving the dimensionality of a given learner. Apparently, the teacher who has asked this question thinks that it is easier (more efficient) to show that at least one set of N+1 points cannot be shattered, than showing it for all.