The product of any three consecutive integers is divisible by 6. Therefore, 3×4×5 (=60), is divisible by 6? Which type of reasoning is embodied here?
Deductive Reasoning
The question asks about the type of reasoning used to conclude that the product of any three consecutive integers is divisible by 6. Specifically, the example given is for 3 × 4 × 5 = 60, which is indeed divisible by 6.
Explanation:
- Consecutive Integers: Consider three consecutive integers \( n, n+1, \) and \( n+2 \).
- Product and Divisibility: The product of these integers is \( n \times (n+1) \times (n+2) \).
- Reasoning:
- Among any three consecutive integers, there will always be exactly one integer that is divisible by 3.
- At least one of these integers (if an even number) will be divisible by 2.
- Thus, the product is divisible by both \( 2 \) and \( 3 \), which implies it is divisible by \( 6 \). This supports our initial claim using logical deduction.
Type of Reasoning:
The reasoning used here is Deductive Reasoning because we start with a general rule or principle (the divisibility of consecutive integers) and apply it to specific instances (the example of 3, 4, and 5).
Let's examine the options:
- Deductive Reasoning: It involves applying a general statement or principle to a specific case. Since we used a general rule about numbers and applied it, this is correct.
- Inductive Reasoning: This is the opposite process—drawing a general conclusion from specific examples, not applicable here.
- Non-verbal Reasoning: This involves recognizing patterns, not relevant in this scenario.
- Abductive Reasoning: This involves creating the best explanation from incomplete information, doesn't apply here.
Conclusion: The correct answer is Deductive Reasoning.
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Important Questions from Deductive
Given below are two statements:
Statement I: No immediate inference can ever be drawn from only one premise.
Statement II: In Aristotelian syllogism, the conclusion is drawn from the first premise through the mediation of the second.
In light of the above statements, choose the correct answer from the options given below:A deductive argument is invalid if:
Given below are some characteristics of reasoning. Select the code that states a characteristic which is not of deductive reasoning:
In which of the following arguments 'the relation that exists between premises and conclusion is that of logical necessity'?
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