Final answer:
Logical entailment is possible without the use of logical connectives, quantification, or equality. Examples include disjunctive syllogism and modus ponens.
Step-by-step explanation:
Logical entailment refers to the relationship between premises and conclusions in a logical argument. It is possible to have logical entailment without using logical connectives, quantification, or equality. One example is the disjunctive syllogism, which states that if one statement is true, then the other statement must be false.
This does not require the use of logical connectives, quantification, or equality. Another example is modus ponens, where if a conditional statement is true and the antecedent is true, then the consequent must also be true. These examples demonstrate that logical entailment is possible without the mentioned logical tools.
Logical entailment typically requires logical connectives and quantification to establish relationships between statements. Conditionals and quantifiers are central to expressing necessary and sufficient conditions, critical to the structure of logical entailment. Removing these tools from logical analysis greatly complicates traditional forms of reasoning.