VIPSolutionsgive answer in 2 step with explanation at the end of each step and final answer at the end:QUESTION 8 The integer 6n is divisible by 4 for all integers n. O True O False
Question:
give answer in 2 step with explanation at the end of each step and final answer at the end:
QUESTION 8
The integer 6n is divisible by 4 for all integers n.
O True
O False
This is AI generated Response.
Asked by: Babu
Created at: 2025-07-11 07:25:46
Asked by: Babu
Created at: 2025-07-11 07:25:46
Final Answer:
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**Step 1:**
Let's analyze the statement "The integer 6n is divisible by 4 for all integers n."
To be divisible by 4, a number must be a multiple of 4. Consider **n = 1**, then 6n = 6 × 1 = 6.
**Explanation:** 6 is not divisible by 4 (6 ÷ 4 = 1.5, not an integer).
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**Step 2:**
Let's try another integer, **n = 2**. Then 6n = 6 × 2 = 12.
**Explanation:** 12 is divisible by 4 (12 ÷ 4 = 3), but the statement says **for all integers n**. Since 6n is not divisible by 4 for n = 1, the statement is **not true for all n**.
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**Final Answer:**
**False**. The integer 6n is **not** divisible by 4 for all integers n.
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