What are some examples of trust and distrust in Lord of the Flies?

One example of trust in Lord of the Flies (though it is misplaced) is when Piggy, understanding himself to be weaker than the other children, tries to ally with Ralph and his cohort. He tries to achieve this by letting Ralph know an embarrassing secret: that people usually denigrate him using the nickname "Piggy." Ralph exploits this for his own gain, immediately announcing it to the tribe. Though Piggy goes on to be Ralph's advisor, this moment helps lead to Piggy's demise, foreshadowed by Jack's later campaign to "hunt Pigs."
An example of distrust is the relationship between Ralph and Jack. They have conflicting agendas on the island: while Ralph wants to establish a form of governance and an ethical code, hoping that they will be rescued, Jack perceives the island as a "survival of the fittest" scenario. As he internalizes the danger of the island, Jack becomes more animalistic and hostile to Ralph, morphing into an antisocial character foil of Ralph and his campaign for society.