Final answer:
The statement 'If Tom goes, then either Bob will go, or neither Mary nor Phillip will go' is represented in logical form by the expression: T → (B ∨ ¬(M ∨ P)). This uses the principles of disjunctive syllogism and the Law of the excluded middle in deductive reasoning.
Step-by-step explanation:
To represent the statement "If Tom goes, then either Bob will go, or neither Mary nor Phillip will go" in logical form, we need to use logical connectors. Let's assume 'T' stands for 'Tom goes', 'B' for 'Bob will go', and 'M ∨ P' meaning 'either Mary goes or Phillip goes'. The statement can then be transformed into a conditional statement combined with a disjunction (or) and a negation (not).
The logical form of the statement would be: T → (B ∨ ¬(M ∨ P)), which reads as 'If T, then B or not both M and P'.
This encapsulates the idea described in the Law of the excluded middle and validates the argument using a form of deductive reasoning, specifically disjunctive syllogism. This form of logic declares that if the premise is true and the first part of the disjunction is false, the second part must be true.