Question

For every natural number a, if aq mod 6 = 3, then a mod 3 does not equal 2?

1) True
2) False

Answer 1

For every natural number a, if aq mod 6 = 3, then a mod 3 does not equal 2.

Step-by-step explanation:

The statement "For every natural number a, if aq mod 6 = 3, then a mod 3 does not equal 2" is true.

To prove this, we can examine the possible values of aq mod 6 for natural numbers a:

• a = 1: 1q mod 6 = 1q = 1
• a = 2: 2q mod 6 = 2q = 2
• a = 3: 3q mod 6 = 3q = 3
• a = 4: 4q mod 6 = 4q = 4
• a = 5: 5q mod 6 = 5q = 5
• a = 6: 6q mod 6 = 0

From these calculations, we can see that aq mod 6 can only equal 3 when a is not a multiple of 3. Therefore, a mod 3 does not equal 2.