There's no such thing as priority, and neither precedence nor associativity define the order in which stuff is evaluated. They determine what is an operand of what operator.

apple && (banana || cherry)
   apple:            LHS operand of &&
   banana || cherry: RHS operand of &&
   banana:           LHS operand of ||
   cherry:           LHS operand of ||

(apple && banana) || cherry
   apple && banana:  LHS operand of ||
   apple:            LHS operand of &&
   banana:           RHS operand of &&
   cherry:           RHS operand of ||
[download]

Operand evaluation order is what controls the order in which stuff is evaluated.

In order to provide short-circuiting, && evaluates its LHS operand before its RHS. Same goes for ||.

Given

apple && (banana || cherry)
   apple:            LHS operand of &&
   banana || cherry: RHS operand of &&
   banana:           LHS operand of ||
   cherry:           LHS operand of ||
[download]

apple must be evaluated before banana || cherry
banana must be evaluated before cherry

So we get:

1. apple
2. banana
3. cherry
4. ||
5. &&

Given

(apple && banana) || cherry
   apple && banana:  LHS operand of ||
   apple:            LHS operand of &&
   banana:           RHS operand of &&
   cherry:           RHS operand of ||
[download]

apple && banana must be evaluated before cherry
apple must be evaluated before banana

So we get:

1. apple
2. banana
3. &&
4. cherry
5. ||

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