Final answer:
It is true that an individual can receive multiple statements via different routes. The assertion that majority rule may not provide a clear outcome with more than two options is also true. Lastly, the statement about wave amplitudes adding up only when propagating in the same line is false; they can interfere and add up at any point they meet.
Step-by-step explanation:
A person may receive multiple statements routed by different means; this is a true statement. In the modern world, information can be disseminated through various channels such as email, postal mail, social media, and more. Due to this multiplicity of channels, it is indeed possible for a person to receive the same or different statements through different routes.
Majority rule can fail to produce a single preferred outcome when there are more than two choices. This is also a true statement. In voting systems or decision-making processes where there are multiple options, majority rule may not always lead to a clear winner because the votes might be spread across more than two options, leading to a situation where no single option receives more than half of the votes.
Regarding the propagation of waves, the statement that the amplitudes of waves add up only if they are propagating in the same line is false. The correct statement is that the amplitudes of two waves can add up through the process of interference, regardless of whether they are propagating in the same line, as long as they meet at the same point.