No supporters of 'party X', who knew Z and supported his campaign strategy, agreed for the alliance with 'party Y'; but some of them had friends in 'party Y'. With reference to the above information, which one among the following statements must be true

The original statement is: "No supporters of 'party X', who knew Z and supported his campaign strategy, agreed for the alliance with 'party Y'; but some of them had friends in 'party Y'." Let's break down the key parts: 1. There exists a group: "supporters of 'party X', who knew Z and supported his campaign strategy." (Let's call this Group A). 2. Group A did not agree to the alliance with 'party Y'. 3. "some of them" (referring to Group A) had friends in 'party Y'. This means at least one person from Group A had a friend who was a supporter of 'party Y'. Now let's evaluate the options: A) Some supporters of 'party Y' did not agree for the alliance with the 'party X'. - The statement tells us about the agreement status of a specific subset of 'party X' supporters. It provides no information about the agreement status of 'party Y' supporters. Therefore, we cannot conclude this must be true. B) There is at least one supporter of 'party Y' who knew some supporters of 'party X' as a friend. - The statement says "some of them [Group A] had friends in 'party Y'." If a person Px from Group A had a friend Py in 'party Y', then by definition, Py (the supporter of 'party Y') knew Px (the supporter of 'party X') as a friend. Since "some of them" implies at least one such Px and Py exist, this statement must be true. C) No supporters of 'party X' supported Z's campaign strategy. - The original statement qualifies a group as "supporters of 'party X', who knew Z and supported his campaign strategy". This phrasing implies that such supporters *do* exist. If no supporters of 'party X' supported Z's campaign strategy, the qualification would be meaningless or the statement would be trivially true in a way that doesn't fit the context. Therefore, this statement contradicts the implied existence of such a group. D) No supporters of 'party X' knew Z. - Similar to C, the original statement refers to "supporters of 'party X', who knew Z". This implies that some supporters of 'party X' *did* know Z. Therefore, this statement contradicts the implied existence of such a group. Conclusion: Only option B can be logically deduced and must be true based on the given information.